This paper analytically derives the Maxwell slip model associated with a frictional rough contact interface using the multi-asperity contact theory in the elastic region. The multi-asperity contact theory based on the Mindlin solution relates interface roughness, material properties, and preload to the contact interface Jenkins element parameters of the discrete Maxwell slip model and continuous Iwan model distribution function. The rough surface properties are obtained from the measured roughness profile of two contacting surfaces. The main advantage of the proposed analytical Maxwell slip model is there is no need to update or identify any parameter using experimental test data. In achieving a rough interface discrete Maxwell slip model, the interface contacting asperities are grouped based on their heights, called a height-region element group of the contact interface model. Each height-region asperities' contact area is divided into annular areas; the number of annular areas determines sliding motion states. Using the classical Mindlin solution, a Jenkins element is assigned to each specified annular area using the Hertzian normal pressure distribution function of the contact area and contribution to the tangential contact stiffness. The Iwan and Maxwell slip model's resultant hysteresis curves are compared with the analytical multi-asperity contact model to verify the proposed contact model procedure's accuracy. Model predictions of the proposed procedure are also validated against measured frictional contact behavior, resulting in good agreements with experimental observations.