Polymeric materials are synthetic macromolecular products, of which, by mechanical or thermal processing, objects of various shapes can be obtained, with wide uses in industry and commerce. This paper deals with the roughness of surfaces obtained during drilling of three polymeric materials: polyamide - PA6, polyacetal - POM-C and high density polyamide - HDPE 1000. In the experimental research was used a EMCO MILL 55 milling machine numerical controlled and HS steel helical drills with two straight cutting edges with the diameter of �8 mm and �10 mm, respectively. Experimental determinations consisted in drilling of the polymeric materials by modifying some parameters of the cutting regime, and determining the roughness of the surface of the holes machined, using the Mitutoyo Surftest SJ-210 rough meter. The purpose of the paper is to predict the roughness of the machined surfaces as one of the important surface quality indicators by using a geometrical model and an artificial neural network (ANN) methodology.