Abstract: The three-dimensional elastic-plastic contact model of the wheel tread system，composed of the conical or worn locomotive wheel and standard rail，is computed by taking the advantage of the finite element parametric quadric programming method．With the analysis of the obtained contact state，force and stress field，the substantial reason of the good wearability of worn types of wheel is pointed out．The presented method offers a new approach for the optimal design of the profiles of wheel and rail．

Key words: Contact, Contact stress, Elastic-plastic, Finite element method, Profiles of wheel and rail