diff --git a/lib/spack/spack/solver/asp.py b/lib/spack/spack/solver/asp.py
index a7c69ae8e3..18c261a317 100644
--- a/lib/spack/spack/solver/asp.py
+++ b/lib/spack/spack/solver/asp.py
@@ -696,6 +696,7 @@ def __init__(self):
         self.possible_virtuals = None
         self.possible_compilers = []
         self.version_constraints = set()
+        self.target_constraints = set()
         self.providers_by_vspec_name = collections.defaultdict(list)
         self.virtual_constraints = set()
         self.compiler_version_constraints = set()
@@ -765,6 +766,16 @@ def spec_versions(self, spec):
         self.version_constraints.add((spec.name, spec.versions))
         return [fn.version_satisfies(spec.name, spec.versions)]
 
+    def target_ranges(self, spec, single_target_fn):
+        target = spec.architecture.target
+
+        # Check if the target is a concrete target
+        if str(target) in archspec.cpu.TARGETS:
+            return [single_target_fn(spec.name, target)]
+
+        self.target_constraints.add((spec.name, target))
+        return [fn.node_target_satisfies(spec.name, target)]
+
     def conflict_rules(self, pkg):
         for trigger, constraints in pkg.conflicts.items():
             for constraint, _ in constraints:
@@ -1167,7 +1178,7 @@ class Body(object):
             if arch.os:
                 clauses.append(f.node_os(spec.name, arch.os))
             if arch.target:
-                clauses.append(f.node_target(spec.name, arch.target))
+                clauses.extend(self.target_ranges(spec, f.node_target))
 
         # variants
         for vname, variant in sorted(spec.variants.items()):
@@ -1437,6 +1448,45 @@ def define_compiler_version_constraints(self):
             )
             self.gen.newline()
 
+    def define_target_constraints(self):
+
+        def _all_targets_satisfiying(single_constraint):
+            allowed_targets = []
+            t_min, _, t_max = single_constraint.partition(':')
+            for test_target in archspec.cpu.TARGETS.values():
+                # Check lower bound
+                if t_min and not t_min <= test_target:
+                    continue
+
+                # Check upper bound
+                if t_max and not t_max >= test_target:
+                    continue
+
+                allowed_targets.append(test_target)
+            return allowed_targets
+
+        cache = {}
+        for spec_name, target_constraint in sorted(self.target_constraints):
+
+            # Construct the list of allowed targets for this constraint
+            allowed_targets = []
+            for single_constraint in str(target_constraint).split(','):
+                if single_constraint not in cache:
+                    cache[single_constraint] = _all_targets_satisfiying(
+                        single_constraint
+                    )
+                allowed_targets.extend(cache[single_constraint])
+
+            allowed_targets = [
+                fn.node_target(spec_name, t) for t in allowed_targets
+            ]
+
+            self.gen.one_of_iff(
+                fn.node_target_satisfies(spec_name, target_constraint),
+                allowed_targets,
+            )
+            self.gen.newline()
+
     def setup(self, driver, specs, tests=False):
         """Generate an ASP program with relevant constraints for specs.
 
@@ -1560,6 +1610,9 @@ def setup(self, driver, specs, tests=False):
         self.gen.h1("Compiler Version Constraints")
         self.define_compiler_version_constraints()
 
+        self.gen.h1("Target Constraints")
+        self.define_target_constraints()
+
     def virtual_spec_clauses(self, dep):
         assert dep.virtual
         self.virtual_constraints.add(str(dep))
diff --git a/lib/spack/spack/test/concretize.py b/lib/spack/spack/test/concretize.py
index 11c2764822..39799fc1bc 100644
--- a/lib/spack/spack/test/concretize.py
+++ b/lib/spack/spack/test/concretize.py
@@ -938,3 +938,8 @@ def test_compiler_match_is_preferred_to_newer_version(self):
 
         assert 'openblas@0.2.13' in s
         assert s['openblas'].satisfies('%gcc@4.4.0')
+
+    @pytest.mark.regression('19981')
+    def test_target_ranges_in_conflicts(self):
+        with pytest.raises(spack.error.SpackError):
+            Spec('impossible-concretization').concretized()
diff --git a/var/spack/repos/builtin.mock/packages/impossible-concretization/package.py b/var/spack/repos/builtin.mock/packages/impossible-concretization/package.py
new file mode 100644
index 0000000000..bb8ad02b49
--- /dev/null
+++ b/var/spack/repos/builtin.mock/packages/impossible-concretization/package.py
@@ -0,0 +1,15 @@
+# Copyright 2013-2020 Lawrence Livermore National Security, LLC and other
+# Spack Project Developers. See the top-level COPYRIGHT file for details.
+#
+# SPDX-License-Identifier: (Apache-2.0 OR MIT)
+class ImpossibleConcretization(Package):
+    """Package that should be impossible to concretize due to a conflict
+    with target ranges. See Issue 19981.
+    """
+
+    homepage = "http://www.example.com"
+    url = "http://www.example.com/example-1.0.tar.gz"
+
+    version(1.0, 'foobarbaz')
+
+    conflicts('target=x86_64:')