In this paper,a theoretical method is proposed to calculate friction force when friction interfaces are constrained to circular motion in a plane.Using this method we can,get the solution of friction force in theory and analyze its features.The comparison of the analytical solution with the numerical one shows that the numerical method is valid.Additionally,the source of errors is analysed in order to provide basis for further application of this method to calculating the friction force when friction interfaces are constrained to complex two-dimensional motions.