The vehicle dynamics and controls play a significant role in vehicle handling performance characteristics. The control of vehicle braking system and wheel slip is a challenging problem due to the nonlinear dynamics of the braking process and the wheel-road interaction. A simple and at the same time realistic vehicle longitudinal braking model is essential for such a challenging problem. In this paper, a new longitudinal rolling/braking quarter-vehicle model is presented. The proposed model takes both the rolling resistance force and the braking force into consideration and investigates their impact on the vehicle longitudinal dynamics. An anti-lock sliding-mode controller is designed to provide wheel slip control during vehicle motion. This type of controller is chosen due to its expected robustness against varying road friction coefficient. Two sliding mode controllers, one using pulse width modulation, and the other a switching controller, are designed and tested using the proposed quarter- vehicle model. The controllers provide an optimal braking torque control which minimize the braking distance by maintaining a desired slip ratio corresponding to the road condition. The simulation results prove the validity of the proposed model and highlights its potential benefits if it is used for the braking control system design problem.