This paper is concerned with the high speed similarity law around affine similarity bodies in inviscid flow. Based on the small-disturbance flow theory, new forms of improved high speed similarity parameters and their applications in analyzing the correlations between the aerodynamic parameters are presented. The main contributions of the new high speed similarity parameters are that they present similarity criteria for two high speed flows if the ratio between the relative thickness (or the conical degree) of the one and that of another one is variable. What is more, these similarity parameters can be used to guide the modeling of aerodynamic parameters for the high speed vehicles with affine similar bodies. In the proof of the new high speed similarity parameters, the dimensionless forms of Euler equations, shock-wave relationships, high speed vehicle surface equations, and boundary conditions are derived. Moreover, the relationships between the aerodynamic parameters of the high speed vehicles with affine bodies are analyzed using the improved high speed similarity parameters.