We　apply　the　first-principles　approach　to　study　the　structural　stability,　Vickers　hardness,　and　elastic　modulus　of　ReB12　and　RuB12.　In　particular,　we　further　investigate　the　influence　of　high　pressure　on　the　structural　stability　and　mechanical　properties　of　ReB12　and　RuB12.　The　calculated　results　show　that　ReB12　and　RuB12　are　thermodynamic　stability　under　high　pressure.　Here,　ReB12　is　more　thermodynamic　stability　than　that　of　the　RuB12.　The　calculated　Vickers　hardness　of　ReB12　and　RuB12　is　16.25　and　16.55　GPa,　respectively.　It　is　found　that　the　calculated　elastic　constants　and　elastic　modulus　of　ReB12　and　RuB12　increase　with　increasing　pressure.　In　particular,　the　calculated　elastic　constants　and　elastic　modulus　of　ReB12　are　larger　than　that　of　the　RuB12.　The　calculated　electronic　structure　shows　that　the　high　hardness　and　elastic　modulus　of　ReB12　and　RuB12　are　attributed　to　the　3D　network　B-B　covalent　bonds.