diff --git a/README.md b/README.md
index 0c5b591e72..504759eabd 100644
--- a/README.md
+++ b/README.md
@@ -199,6 +199,10 @@ up the sysroot.  If you are using `miri` (the Miri driver) directly, see the
 Miri adds its own set of `-Z` flags, which are usually set via the `MIRIFLAGS`
 environment variable:
 
+* `-Zmiri-check-number-validity` enables checking of integer and float validity
+  (e.g., they must be initialized and not carry pointer provenance) as part of
+  enforcing validity invariants. This has no effect when
+  `-Zmiri-disable-validation` is present.
 * `-Zmiri-compare-exchange-weak-failure-rate=<rate>` changes the failure rate of
   `compare_exchange_weak` operations. The default is `0.8` (so 4 out of 5 weak ops will fail).
   You can change it to any value between `0.0` and `1.0`, where `1.0` means it
diff --git a/rust-version b/rust-version
index fd8c69e112..d43b9e8197 100644
--- a/rust-version
+++ b/rust-version
@@ -1 +1 @@
-db062de72b0a064f45b6f86894cbdc7c0ec68844
+68ca579406f2fa9ec62710e4a4d5d3e07a168d3c
diff --git a/src/bin/miri.rs b/src/bin/miri.rs
index 84e66db2a7..cf32e63322 100644
--- a/src/bin/miri.rs
+++ b/src/bin/miri.rs
@@ -313,6 +313,9 @@ fn main() {
                 "-Zmiri-symbolic-alignment-check" => {
                     miri_config.check_alignment = miri::AlignmentCheck::Symbolic;
                 }
+                "-Zmiri-check-number-validity" => {
+                    miri_config.check_number_validity = true;
+                }
                 "-Zmiri-disable-abi-check" => {
                     miri_config.check_abi = false;
                 }
diff --git a/src/eval.rs b/src/eval.rs
index 5d8d332fcd..ac32af30c1 100644
--- a/src/eval.rs
+++ b/src/eval.rs
@@ -66,6 +66,8 @@ pub struct MiriConfig {
     pub stacked_borrows: bool,
     /// Controls alignment checking.
     pub check_alignment: AlignmentCheck,
+    /// Controls integer and float validity (e.g., initialization) checking.
+    pub check_number_validity: bool,
     /// Controls function [ABI](Abi) checking.
     pub check_abi: bool,
     /// Action for an op requiring communication with the host.
@@ -104,6 +106,7 @@ impl Default for MiriConfig {
             validate: true,
             stacked_borrows: true,
             check_alignment: AlignmentCheck::Int,
+            check_number_validity: false,
             check_abi: true,
             isolated_op: IsolatedOp::Reject(RejectOpWith::Abort),
             ignore_leaks: false,
diff --git a/src/machine.rs b/src/machine.rs
index 23278a4891..0ead28b36c 100644
--- a/src/machine.rs
+++ b/src/machine.rs
@@ -304,6 +304,9 @@ pub struct Evaluator<'mir, 'tcx> {
     /// Whether to enforce the validity invariant.
     pub(crate) validate: bool,
 
+    /// Whether to enforce validity (e.g., initialization) of integers and floats.
+    pub(crate) enforce_number_validity: bool,
+
     /// Whether to enforce [ABI](Abi) of function calls.
     pub(crate) enforce_abi: bool,
 
@@ -356,6 +359,7 @@ impl<'mir, 'tcx> Evaluator<'mir, 'tcx> {
             tls: TlsData::default(),
             isolated_op: config.isolated_op,
             validate: config.validate,
+            enforce_number_validity: config.check_number_validity,
             enforce_abi: config.check_abi,
             file_handler: Default::default(),
             dir_handler: Default::default(),
@@ -426,6 +430,11 @@ impl<'mir, 'tcx> Machine<'mir, 'tcx> for Evaluator<'mir, 'tcx> {
         ecx.machine.validate
     }
 
+    #[inline(always)]
+    fn enforce_number_validity(ecx: &InterpCx<'mir, 'tcx, Self>) -> bool {
+        ecx.machine.enforce_number_validity
+    }
+
     #[inline(always)]
     fn enforce_abi(ecx: &InterpCx<'mir, 'tcx, Self>) -> bool {
         ecx.machine.enforce_abi
diff --git a/src/shims/posix/sync.rs b/src/shims/posix/sync.rs
index 782765c778..606f58a207 100644
--- a/src/shims/posix/sync.rs
+++ b/src/shims/posix/sync.rs
@@ -1,5 +1,8 @@
 use std::time::SystemTime;
 
+use rustc_hir::LangItem;
+use rustc_middle::ty::{layout::TyAndLayout, query::TyCtxtAt, subst::Subst, Ty};
+
 use crate::*;
 use thread::Time;
 
@@ -44,7 +47,7 @@ fn mutexattr_set_kind<'mir, 'tcx: 'mir>(
     attr_op: &OpTy<'tcx, Tag>,
     kind: impl Into<ScalarMaybeUninit<Tag>>,
 ) -> InterpResult<'tcx, ()> {
-    ecx.write_scalar_at_offset(attr_op, 0, kind, ecx.machine.layouts.i32)
+    ecx.write_scalar_at_offset(attr_op, 0, kind, layout_of_maybe_uninit(ecx.tcx, ecx.tcx.types.i32))
 }
 
 // pthread_mutex_t is between 24 and 48 bytes, depending on the platform.
@@ -79,7 +82,7 @@ fn mutex_set_kind<'mir, 'tcx: 'mir>(
         mutex_op,
         offset,
         kind,
-        ecx.machine.layouts.i32,
+        layout_of_maybe_uninit(ecx.tcx, ecx.tcx.types.i32),
         AtomicWriteOp::Relaxed,
     )
 }
@@ -100,7 +103,7 @@ fn mutex_set_id<'mir, 'tcx: 'mir>(
         mutex_op,
         4,
         id,
-        ecx.machine.layouts.u32,
+        layout_of_maybe_uninit(ecx.tcx, ecx.tcx.types.u32),
         AtomicWriteOp::Relaxed,
     )
 }
@@ -144,7 +147,7 @@ fn rwlock_set_id<'mir, 'tcx: 'mir>(
         rwlock_op,
         4,
         id,
-        ecx.machine.layouts.u32,
+        layout_of_maybe_uninit(ecx.tcx, ecx.tcx.types.u32),
         AtomicWriteOp::Relaxed,
     )
 }
@@ -211,7 +214,7 @@ fn cond_set_id<'mir, 'tcx: 'mir>(
         cond_op,
         4,
         id,
-        ecx.machine.layouts.u32,
+        layout_of_maybe_uninit(ecx.tcx, ecx.tcx.types.u32),
         AtomicWriteOp::Relaxed,
     )
 }
@@ -244,7 +247,12 @@ fn cond_set_clock_id<'mir, 'tcx: 'mir>(
     cond_op: &OpTy<'tcx, Tag>,
     clock_id: impl Into<ScalarMaybeUninit<Tag>>,
 ) -> InterpResult<'tcx, ()> {
-    ecx.write_scalar_at_offset(cond_op, 8, clock_id, ecx.machine.layouts.i32)
+    ecx.write_scalar_at_offset(
+        cond_op,
+        8,
+        clock_id,
+        layout_of_maybe_uninit(ecx.tcx, ecx.tcx.types.i32),
+    )
 }
 
 /// Try to reacquire the mutex associated with the condition variable after we
@@ -788,3 +796,12 @@ pub trait EvalContextExt<'mir, 'tcx: 'mir>: crate::MiriEvalContextExt<'mir, 'tcx
         Ok(0)
     }
 }
+
+fn layout_of_maybe_uninit<'tcx>(tcx: TyCtxtAt<'tcx>, param: Ty<'tcx>) -> TyAndLayout<'tcx> {
+    let def_id = tcx.require_lang_item(LangItem::MaybeUninit, None);
+    let def_ty = tcx.type_of(def_id);
+    let ty = def_ty.subst(*tcx, &[param.into()]);
+
+    let param_env = tcx.param_env(def_id);
+    tcx.layout_of(param_env.and(ty)).unwrap()
+}
diff --git a/tests/compile-fail/uninit_float.rs b/tests/compile-fail/uninit_float.rs
new file mode 100644
index 0000000000..06953e1ced
--- /dev/null
+++ b/tests/compile-fail/uninit_float.rs
@@ -0,0 +1,8 @@
+// compile-flags: -Zmiri-check-number-validity
+
+// This test is adapted from https://github.com/rust-lang/miri/issues/1340#issue-600900312.
+
+fn main() {
+    let _val = unsafe { std::mem::MaybeUninit::<f32>::uninit().assume_init() };
+    //~^ ERROR type validation failed at .value: encountered uninitialized bytes, but expected initialized plain (non-pointer) bytes
+}
diff --git a/tests/compile-fail/uninit_integer.rs b/tests/compile-fail/uninit_integer.rs
new file mode 100644
index 0000000000..757f69c050
--- /dev/null
+++ b/tests/compile-fail/uninit_integer.rs
@@ -0,0 +1,8 @@
+// compile-flags: -Zmiri-check-number-validity
+
+// This test is from https://github.com/rust-lang/miri/issues/1340#issue-600900312.
+
+fn main() {
+    let _val = unsafe { std::mem::MaybeUninit::<usize>::uninit().assume_init() };
+    //~^ ERROR type validation failed at .value: encountered uninitialized bytes, but expected initialized plain (non-pointer) bytes
+}
diff --git a/tests/compile-fail/uninit_integer_signed.rs b/tests/compile-fail/uninit_integer_signed.rs
new file mode 100644
index 0000000000..bb5d7314a7
--- /dev/null
+++ b/tests/compile-fail/uninit_integer_signed.rs
@@ -0,0 +1,8 @@
+// compile-flags: -Zmiri-check-number-validity
+
+// This test is adapted from https://github.com/rust-lang/miri/issues/1340#issue-600900312.
+
+fn main() {
+    let _val = unsafe { std::mem::MaybeUninit::<i32>::uninit().assume_init() };
+    //~^ ERROR type validation failed at .value: encountered uninitialized bytes, but expected initialized plain (non-pointer) bytes
+}
diff --git a/tests/compile-fail/uninit_raw_ptr.rs b/tests/compile-fail/uninit_raw_ptr.rs
new file mode 100644
index 0000000000..beb9ad1270
--- /dev/null
+++ b/tests/compile-fail/uninit_raw_ptr.rs
@@ -0,0 +1,4 @@
+fn main() {
+    let _val = unsafe { std::mem::MaybeUninit::<*const u8>::uninit().assume_init() };
+    //~^ ERROR type validation failed at .value: encountered uninitialized raw pointer
+}
diff --git a/tests/run-pass/uninit_number_ignored.rs b/tests/run-pass/uninit_number_ignored.rs
new file mode 100644
index 0000000000..77d6af6e99
--- /dev/null
+++ b/tests/run-pass/uninit_number_ignored.rs
@@ -0,0 +1,8 @@
+// This test is adapted from https://github.com/rust-lang/miri/issues/1340#issue-600900312.
+// This test passes because -Zmiri-check-number-validity is not passed.
+
+fn main() {
+    let _val1 = unsafe { std::mem::MaybeUninit::<usize>::uninit().assume_init() };
+    let _val2 = unsafe { std::mem::MaybeUninit::<i32>::uninit().assume_init() };
+    let _val3 = unsafe { std::mem::MaybeUninit::<f32>::uninit().assume_init() };
+}