Abstract: The similarty rules are based on general aerodynamic similarity theory and drived for the transformation between transonic and subsonic flows,transonic and incompressible flows,and subsonic and incompressible flows respectively,as well as in the cases of full disturbance,according to the linear small perturbation theory,the transonic small perturbation theory and the full potential equation.The validity of the similarity transformations under the inviscid assumption is verified by two dimensional and quasi three dimensional numerical simulations.The reasonableness of the basic concepts and assumptions used in the present work,such as local linearization concept,are testified by the numerical expeiments as well.This work provides an essential basis for the similarity transformation between the high and low spee models of high pressure axial compressors,and offers an approach to the profile design of a similarity low speed model and to applieation of experimental data of the similarity low speed model to the high speed high pressure axial compressor bladings.