An investigation of the mechanics of orthogonal cutting on an acetal resin (Delrin 150x) plastic and a nylon resin (Zytel 101) plastic was carried out. The specimens were in the form of tubes and the rake angles and feeds were varied from −10 to +40 deg and 0.003 to 0.0115 ipr, respectively. It was found that a shear-plane type of analysis and the minimum-energy principle at low tool chip contact friction are applicable. It was found further that some of the reasons for the formation of discontinuous chips for Delrin 150x were excessive strains and induction of tensile stresses into the zone ahead of the tool. By the use of the minimum-energy principle and a constant dynamic shear stress, which appears to correlate with static properties, it was possible to predict the tool forces for Zytel 101 to a satisfactory degree of accuracy.