A high friction coefficient is first observed as sliding between bodies commences, which is called static frictionStatic friction. Subsequently, the friction coefficient decreases and approaches the lowest stationary value, which is called kinetic frictionKinetic friction. Thereafter, if the sliding stops for a while and then starts again, the friction coefficient recovers and a behavior similar to that of the first sliding is reproduced. In this article, the friction coefficient is considered as a state variable, and its evolution law is discussed. Subsequently, based on the elastoplastic theory, a constitutive model for friction is developed to describe the aforementioned rate- and state-dependent frictional sliding behaviors. The response characteristics of the rate-dependent subloading surface model and its capability to describe the experimental results are demonstrated. Furthermore, its basic characteristics are summarized.