The increasing diffusion of Metal Matrix Composites (MMC) materials has pointed out the limits of the traditional chip removal manufacturing processes and has encouraged the study of innovative processes, such as Abrasive Water Jet (AWJ). A critical aspect of AWJ machining is the quality of the cutting surfaces. In fact, the AWJ surfaces present a wide dispersion of micro geometrical characteristics depending both on the process variables and on the cutting depth. Thus, the morphology of the kerf surfaces can be altered acting on the cutting variables. The present work reports an experimental study of the influence of AWJ process variables on the surface finish of MMC cuts. Some statistical tools (Analysis of Variance - ANOVA - and analysis of regression) have been used to quantify and then to formalize the empirical relationships between the process variables and the surface parameters along the surface. Two linear regression models are presented, which can be used to predict the surface finish. These models represent the first step in the control of the quality of the cutting results aiming to the optimization of the machining, for the full exploitation of the MMC cutting by means of this non traditional manufacturing process.