Abstract: This paper under takes the geometrical analysis of Railway trasiton spiral(R.T.S)tooth shape as follows.1) to solve the RTS tooth shope equation by means of the diagrammetic limited elements anlysis.2) The arrangment of asymptotes, normal field and Pith Lines for R. T. S tooth shape.3) Deducing the eguation of the path of tooth flank contact tooth shape,the tem orary Contaet Line and the transverse contact ratio by means of the basic rack principle.4) The sensitivity of R. T. S tooth Shape to the error of canter distance.5) The mian points of R. T. S tooth profile design.