The abrasive flow machining (AFM) process can be applied to an impressive range of finishing operations, providing uniform, repeatable and predictive results. It offers higher productivity, automation, flexibility and ability to control the intensity and location of machining. In the literature there is not much information available that deals with the theoretical analysis of AFM process. A finite element model has been proposed for analysing the flow of a viscoelastic medium in the AFM process. The results of the finite element analysis have been used to estimate the material removal and surface finish in AFM process. Experiments have been planned using a central composite rotatable design to obtain useful inferences by performing the minimum number of experiments. The theoretical results obtained by the finite element simulation have been compared with experimental results. The effects of the process parameters on the process performance have been discussed.