Quartz　crystal　has　excellent　piezoelectric　properties,　it　can　be　used　as　substrates　of　surface　acoustic　wave　(SAW)　devices,　for　example　delay　line,　filter,　oscillator,　convolver,　acousto-optic　(AO)　device　and　so　on.　In　this　paper,　Intrinsic　SAW　basic　equation　group　and　SAW　mechanical　boundary　condition　equation　group　are　deduced　from　character　equation　of　the　crystal.　Intrinsic　SAW　velocities　are　calculated　using　circle　iterative　method　in　three　coordinate　planes　of　quartz　crystal　systematically.　Stiffness　coefficient　of　piezoelectric　crystal　can　be　changed　by　piezoelectric　effect　and　it　is　named　as　piezoelectric　modified　stiffness　coefficient.　Reciprocal　velocity　curves　of　quartz　crystal　in　the　three　coordinate　planes　using　the　non-modified　stiffness　coefficients　and　the　piezoelectric　modified　stiffness　coefficients　are　drawn　respectively.　Configurations　and　periods　of　the　curves　are　similar　to　projection　figures　of　crystal　lattice　of　the　triangle　crystal　system　in　same　coordinate　planes.　It　means　that　there　is　internal　relationship　between　the　SAW　properties　and　point　group　symmetries　of　the　crystal.　Research　results　lay　a　solid　base　for　design　and　manufacture　of　the　SAW　device.　It　has　theoretical　significance　and　practical　value.