diff --git a/hail/python/hail/expr/__init__.py b/hail/python/hail/expr/__init__.py
index bff07932fd9..37d82d3117f 100644
--- a/hail/python/hail/expr/__init__.py
+++ b/hail/python/hail/expr/__init__.py
@@ -218,6 +218,8 @@
     rand_gamma,
     rand_int32,
     rand_int64,
+    rand_hyper,
+    rand_multi_hyper,
     rand_norm,
     rand_norm2d,
     rand_pois,
@@ -395,6 +397,8 @@
     'rand_gamma',
     'rand_cat',
     'rand_dirichlet',
+    'rand_hyper',
+    'rand_multi_hyper',
     'sqrt',
     'corr',
     'str',
diff --git a/hail/python/hail/expr/functions.py b/hail/python/hail/expr/functions.py
index 0558be5d0f5..bce627436f4 100644
--- a/hail/python/hail/expr/functions.py
+++ b/hail/python/hail/expr/functions.py
@@ -3300,6 +3300,16 @@ def rand_dirichlet(a, seed=None) -> ArrayExpression:
     return hl.bind(lambda x: x / hl.sum(x), a.map(lambda p: hl.if_else(p == 0.0, 0.0, hl.rand_gamma(p, 1, seed=seed))))
 
 
+@typecheck(ngood=expr_int32, nbad=expr_int32, nsample=expr_int32, seed=nullable(int))
+def rand_hyper(ngood, nbad, nsample, seed=None) -> Int32Expression:
+    return _seeded_func("rand_hyper", tint32, seed, ngood, nbad, nsample)
+
+
+@typecheck(colors=expr_array(expr_int32), nsample=expr_int32, seed=nullable(int))
+def rand_multi_hyper(colors, nsample, seed=None) -> Int32Expression:
+    return _seeded_func("rand_multi_hyper", tarray(tint32), seed, colors, nsample)
+
+
 @typecheck(x=oneof(expr_float64, expr_ndarray(expr_float64)))
 @ndarray_broadcasting
 def sqrt(x) -> Float64Expression:
diff --git a/hail/python/test/hail/expr/test_expr.py b/hail/python/test/hail/expr/test_expr.py
index 1a9477533e7..af09796cb7a 100644
--- a/hail/python/test/hail/expr/test_expr.py
+++ b/hail/python/test/hail/expr/test_expr.py
@@ -69,6 +69,8 @@ def test_random_function(rand_f):
         test_random_function(lambda: hl.rand_gamma(1, 1))
         test_random_function(lambda: hl.rand_cat(hl.array([1, 1, 1, 1])))
         test_random_function(lambda: hl.rand_dirichlet(hl.array([1, 1, 1, 1])))
+        test_random_function(lambda: hl.rand_hyper(5, 10, 4))
+        test_random_function(lambda: hl.rand_multi_hyper([5, 2, 8], 4))
 
     def test_range(self):
         def same_as_python(*args):
diff --git a/hail/src/main/scala/is/hail/expr/ir/functions/RandomSeededFunctions.scala b/hail/src/main/scala/is/hail/expr/ir/functions/RandomSeededFunctions.scala
index 9ba56ad97b6..39917358e44 100644
--- a/hail/src/main/scala/is/hail/expr/ir/functions/RandomSeededFunctions.scala
+++ b/hail/src/main/scala/is/hail/expr/ir/functions/RandomSeededFunctions.scala
@@ -389,6 +389,74 @@ object RandomSeededFunctions extends RegistryFunctions {
         primitive(cb.memoize(rng.invoke[Double, Double, Double]("rgamma", a.value, scale.value)))
     }
 
+    registerSCode4(
+      "rand_hyper",
+      TRNGState,
+      TInt32,
+      TInt32,
+      TInt32,
+      TInt32,
+      {
+        case (_: Type, _: SType, _: SType, _: SType, _: SType) => SInt32
+      },
+    ) {
+      case (
+            _,
+            cb,
+            _,
+            rngState: SRNGStateValue,
+            nGood: SInt32Value,
+            nBad: SInt32Value,
+            nSample: SInt32Value,
+            _,
+          ) =>
+        val rng = cb.emb.getThreefryRNG()
+        rngState.copyIntoEngine(cb, rng)
+        primitive(cb.memoize(rng.invoke[Double, Double, Double, Double](
+          "rhyper",
+          nGood.value.toD,
+          nBad.value.toD,
+          nSample.value.toD,
+        ).toI))
+    }
+
+    registerSCode3(
+      "rand_multi_hyper",
+      TRNGState,
+      TArray(TInt32),
+      TInt32,
+      TArray(TInt32),
+      {
+        case (_: Type, _: SType, _: SType, _: SType) =>
+          SIndexablePointer(PCanonicalArray(PInt32(required = true)))
+      },
+    ) {
+      case (r, cb, _, rngState: SRNGStateValue, colors: SIndexableValue, nSample: SInt32Value, _) =>
+        val rng = cb.emb.getThreefryRNG()
+        rngState.copyIntoEngine(cb, rng)
+        val (push, finish) = PCanonicalArray(PInt32(required = true))
+          .constructFromFunctions(cb, r.region, colors.loadLength(), deepCopy = false)
+        cb.if_(
+          colors.hasMissingValues(cb),
+          cb._fatal("rand_multi_hyper: colors may not contain missing values"),
+        )
+        val remaining = cb.newLocal[Int]("rand_multi_hyper_N", 0)
+        val toSample = cb.newLocal[Int]("rand_multi_hyper_toSample", nSample.value)
+        colors.forEachDefined(cb)((cb, _, n) => cb.assign(remaining, remaining + n.asInt.value))
+        colors.forEachDefined(cb) { (cb, _, n) =>
+          cb.assign(remaining, remaining - n.asInt.value)
+          val drawn = cb.memoize(rng.invoke[Double, Double, Double, Double](
+            "rhyper",
+            n.asInt.value.toD,
+            remaining.toD,
+            toSample.toD,
+          ).toI)
+          cb.assign(toSample, toSample - drawn)
+          push(cb, IEmitCode.present(cb, primitive(drawn)))
+        }
+        finish(cb)
+    }
+
     registerSCode2(
       "rand_cat",
       TRNGState,