In the present study, a phenomenological rate-dependent friction model is implemented in the dynamic finite element method. Typical frictional contact problems, which are consisted by elastic and rigid bodies having simple shapes, are then analyzed by the present method. The validity of the present method for the analysis of stick-slip motion under dry condition is examined. It is shown that the present method can solve stick-slip motion within the framework of continuum mechanics, whereas it cannot predict by the conventional finite element method based on the rate-independent friction model.