Abstract: In many cases the modeling of machining and deformation processes may be based on a rigid plastic material model. The yield criterion of some plastically incompressible metallic materials depends on the hydrostatic stress. The double shearing model can be used to describe the behavior of such materials. As a rule, friction occurs in machining and deformation processes. One of widely used friction law is the maximum friction law. In the case of the double shearing model this law demands that the friction surface coincides with an envelope of characteristics. The present study deals with the effect of this friction law on the temperature field in the vicinity of the friction surface. The study is restricted to stationary planar flows. In particular, the behavior of the temperature field near the maximum friction surface is found from asymptotic analysis of the systems of equations of thermoplasticity. It is shown that the plastic work rate follows an inverse square root rule near maximum friction surfaces and thus, approaches infinity at the surface. Since, the plastic work rate is involved in the heat conduction equation, the temperature and the heat flux must be describable by nondifferentiable functions where the singular behavior of the plastic work occurs. It is hypothesized that the asymptotic analysis performed can be useful for predicting the generation of white layers in machining processes and fine grain layers in deformation processes.