This paper presents a study of the stresses and temperatures developed in the region near the tip of the toot in the orthogonal machining problem. The flow field is approximated by that which exists in a perfect fluid that occupies the same spatial region as the work material and is studied by the conformal mapping technique. This mapping yieldx the flow lines and strain rates in parametric form. After the kinematics has been evaluated, the material is assumed to be a nonlinearly viscous substance that deforms along the same flow lines as those in a perfect fluid. Stresses and temperatures are calculated for the case of zero friction along the tool-work piece interface. Heating is due to the conversion of plastic work into heat and conduction is ignored. The case of zero rake angle is discussed in detail.