This paper deals with a rigid-plastic finite element method (FEM) of chip formation process in an orthogonal cutting of single crystal metals. Yield function of single crystal based on the Schmid's law is introduced in the rigid-plastic FEM by applying maximum plastic work principle. A new FEM model is proposed to analyze the chip formation process from the initial state to steady state on the basis of both crystal characteristics and cutting conditions. In the model, the elements of the workpiece are remeshed when the tool moves against the workpieces in order to simulate the chip separation during the cutting process. The FEM model proposed here is applied to the analysis of the micro cutting process of single crystal copper, and the results are compared with the experimental results. The results of FEM analysis, such as shapes of chips, shear angles and specific cutting forces, are in good agreement with the experimental results.