During the last decade the abrasive flow machining process became an accepted technique to smooth and to round inner edges in badly contactable regions of complex geometries, e.g. grooves in rails of common rail systems. The process is based on the flow of a highly viscous silicone oil which is charged by abrasive particles. This leads to an efficient rounding of the egdes. In the present article a material model for the non-Newtonian behaviour of the abrasive paste is proposed, the material parameters are identified according to experiments and, finally, a simulation of the abrasive flow machining process is presented based on a model implementation in the software package COMSOL Multiphysics®.