The strain rate intensity factor is the coefficient of the leading singular term in a series expansion of the equivalent strain rate in the vicinity of maximum friction surfaces. In the case of rigid perfectly plastic solids, the maximum friction law postulates that the friction stress at sliding is equal to the shear yield stress. The equivalent strain rate approaches infinity near maximum friction surfaces. Therefore, the strain rate intensity factor cannot be calculated by means of standard finite element packages. On the other hand, the strain rate intensity factor can be used to predict the generation of fine grain layers in the vicinity of friction surfaces in metal forming processes. In order to develop a model that connects the strain rate intensity factor and parameters characterizing such layers, it is necessary to propose a numerical method for calculating the strain rate intensity factor with a high accuracy. In the present paper, the strain rate intensity factor is expressed in terms of quantities that are found by means of conventional numerical methods based on the theory of characteristics. Then, an available numerical method is complemented with an additional procedure to find the strain rate intensity factor. The new method is used to calculate the strain rate intensity factor in compression of a plastic layer between parallel plates. The approach proposed is restricted to plane strain deformation of rigid perfectlyplastic material.