Abrasive processes, commonly employed in manufacturing, are difficult to model because they rely on brittle particles with unknown geometry and multiple points of contact. Newly developed microreplicated abrasives allow for control of abrasive grit properties such as size, shape, and distribution. This paper proposes and validates a parametric model of abrasive machining that allows for studying the interaction of this particular tooling with randomly generated surfaces. In this work, the parameters of a probability distribution function that represents the workpiece surface are approximated by profilometry data. Monte Carlo simulation is used to account for inter- and intraspecimen variability. A geometric representation is used to mathematically represent the interaction between workpiece and tool. The results show good correlation between theoretical and actual values. This approach could be used to aid in tool geometry design as well as in process parameter optimization.