diff --git a/Library/Homebrew/os/linux/elf.rb b/Library/Homebrew/os/linux/elf.rb
index 8eeae1fc5e..9376bdf047 100644
--- a/Library/Homebrew/os/linux/elf.rb
+++ b/Library/Homebrew/os/linux/elf.rb
@@ -149,6 +149,7 @@ module ELFShim
 
       # Search for dependencies in the runpath/rpath first
       local_paths&.each do |local_path|
+        local_path = OS::Linux::Elf.expand_elf_dst(local_path, "ORIGIN", path.parent)
         candidate = Pathname(local_path)/basename
         return candidate if candidate.exist? && candidate.elf?
       end
@@ -221,3 +222,37 @@ module ELFShim
     metadata.dylibs
   end
 end
+
+module OS
+  module Linux
+    # Helper functions for working with ELF objects.
+    #
+    # @api private
+    module Elf
+      sig { params(str: String, ref: String, repl: T.any(String, Pathname)).returns(String) }
+      def self.expand_elf_dst(str, ref, repl)
+        # ELF gABI rules for DSTs:
+        #   - Longest possible sequence using the rules (greedy).
+        #   - Must start with a $ (enforced by caller).
+        #   - Must follow $ with one underscore or ASCII [A-Za-z] (caller
+        #     follows these rules for REF) or '{' (start curly quoted name).
+        #   - Must follow first two characters with zero or more [A-Za-z0-9_]
+        #     (enforced by caller) or '}' (end curly quoted name).
+        # (from https://github.com/bminor/glibc/blob/41903cb6f460d62ba6dd2f4883116e2a624ee6f8/elf/dl-load.c#L182-L228)
+
+        # In addition to capturing a token, also attempt to capture opening/closing braces and check that they are not
+        # mismatched before expanding.
+        str.gsub(/\$({?)([a-zA-Z_][a-zA-Z0-9_]*)(}?)/) do |orig_str|
+          has_opening_brace = ::Regexp.last_match(1).present?
+          matched_text = ::Regexp.last_match(2)
+          has_closing_brace = ::Regexp.last_match(3).present?
+          if (matched_text == ref) && (has_opening_brace == has_closing_brace)
+            repl
+          else
+            orig_str
+          end
+        end
+      end
+    end
+  end
+end
diff --git a/Library/Homebrew/test/os/linux/elf_spec.rb b/Library/Homebrew/test/os/linux/elf_spec.rb
new file mode 100644
index 0000000000..6bcf15f0a9
--- /dev/null
+++ b/Library/Homebrew/test/os/linux/elf_spec.rb
@@ -0,0 +1,87 @@
+# frozen_string_literal: true
+
+RSpec.describe OS::Linux::Elf do
+  describe "::expand_elf_dst" do
+    it "expands tokens that are not wrapped in curly braces" do
+      str = "$ORIGIN/../lib"
+      ref = "ORIGIN"
+      repl = "/opt/homebrew/bin"
+      expected = "/opt/homebrew/bin/../lib"
+      expect(described_class.expand_elf_dst(str, ref, repl)).to eq(expected)
+    end
+
+    it "expands tokens that are wrapped in curly braces" do
+      str = "${ORIGIN}/../lib"
+      ref = "ORIGIN"
+      repl = "/opt/homebrew/bin"
+      expected = "/opt/homebrew/bin/../lib"
+      expect(described_class.expand_elf_dst(str, ref, repl)).to eq(expected)
+
+      str = "${ORIGIN}new/../lib"
+      ref = "ORIGIN"
+      repl = "/opt/homebrew/bin"
+      expected = "/opt/homebrew/binnew/../lib"
+      expect(described_class.expand_elf_dst(str, ref, repl)).to eq(expected)
+    end
+
+    it "expands multiple occurrences of token" do
+      str = "${ORIGIN}/../..$ORIGIN/../lib"
+      ref = "ORIGIN"
+      repl = "/opt/homebrew/bin"
+      expected = "/opt/homebrew/bin/../../opt/homebrew/bin/../lib"
+      expect(described_class.expand_elf_dst(str, ref, repl)).to eq(expected)
+    end
+
+    it "rejects and passes through tokens containing additional characters" do
+      str = "$ORIGINAL/../lib"
+      ref = "ORIGIN"
+      repl = "/opt/homebrew/bin"
+      expected = "$ORIGINAL/../lib"
+      expect(described_class.expand_elf_dst(str, ref, repl)).to eq(expected)
+
+      str = "$ORIGIN_/../lib"
+      ref = "ORIGIN"
+      repl = "/opt/homebrew/bin"
+      expected = "$ORIGIN_/../lib"
+      expect(described_class.expand_elf_dst(str, ref, repl)).to eq(expected)
+
+      str = "$ORIGIN_STORY/../lib"
+      ref = "ORIGIN"
+      repl = "/opt/homebrew/bin"
+      expected = "$ORIGIN_STORY/../lib"
+      expect(described_class.expand_elf_dst(str, ref, repl)).to eq(expected)
+
+      str = "${ORIGINAL}/../lib"
+      ref = "ORIGIN"
+      repl = "/opt/homebrew/bin"
+      expected = "${ORIGINAL}/../lib"
+      expect(described_class.expand_elf_dst(str, ref, repl)).to eq(expected)
+
+      str = "${ORIGIN_}/../lib"
+      ref = "ORIGIN"
+      repl = "/opt/homebrew/bin"
+      expected = "${ORIGIN_}/../lib"
+      expect(described_class.expand_elf_dst(str, ref, repl)).to eq(expected)
+
+      str = "${ORIGIN_STORY}/../lib"
+      ref = "ORIGIN"
+      repl = "/opt/homebrew/bin"
+      expected = "${ORIGIN_STORY}/../lib"
+      expect(described_class.expand_elf_dst(str, ref, repl)).to eq(expected)
+    end
+
+    it "rejects and passes through tokens with mismatched curly braces" do
+      str = "${ORIGIN/../lib"
+      ref = "ORIGIN"
+      repl = "/opt/homebrew/bin"
+      expected = "${ORIGIN/../lib"
+      expect(described_class.expand_elf_dst(str, ref, repl)).to eq(expected)
+
+      str = "$ORIGIN}/../lib"
+      ref = "ORIGIN"
+      repl = "/opt/homebrew/bin"
+      expected = "$ORIGIN}/../lib"
+      expect(described_class.expand_elf_dst(str, ref, repl)).to eq(expected)
+    end
+  end
+end