A vehicle longitudinal control strategy with guaranteed string stability for vehicle stop-and-go(SG) cruise control is presented in this paper. The SG cruise control systems should be designed such that string stability can be guaranteed in addition to that every vehicle in a string of SG cruise control vehicles must track any bounded acceleration and velocity profile of its preceding vehicle with a bounded spacing and velocity error. An optimal vehicle following control law based on the information of the 1311owing distance (clearance) and its velocity relative to the vehicle ahead (relative velocity) has been used and string stability analysis has been done based on the control law and constant time gap spacing policy, A validated multi-vehicle simulation package has been shown that the string stability analysis using the approximate model of the vehicle servo-loop which includes vehicle powertrain and brake control system dynamics is valid in the design of the SG cruise control law with guaranteed string stability.