The　local-density　approximation　(LDA)　coupled　with　the　virtual　crystal　approximation　(VCA)　method　electronic　structure　is　applied　to　evaluate　elastic　constants,　bulk　modulus,　shear　modulus,　Young＇s　modulus　and　Poisson＇s　ratio　mechanic　properties　of　metal　zirconium,　Zircaloy-2　and　Zircaloy-4.　The　results　show　that　there　is　no　obvious　difference　in　band　structure　and　total　density　of　state　(DOS)　between　metal　zirconium　and　zirconium　alloy.　However,　p　and　d　electron　partial　density　of　state　(PDOS)　presents　the　slight　difference　between　metal　zirconium　and　zirconium　alloy.　Zircaloy-2　and　Zircaloy-4　present　better　elastic　mechanical　properties　than　metal　zirconium.　The　metal　zirconium　and　zirconium　alloy　show　the　anisotropic　mechanical　properties.