We consider the car-following model introduced by P G Gipps (1981). This model is of practical importance as it powers the UK Transport Research Laboratory highway simulation package SISTM. Firstly, a brief derivation of the model is given in simplified circumstances. Second, we show how uniform flow solutions and a speed-headway function may be derived. Finally, we consider the linear stability of uniform flow solutions. Conditions for stability and onset of instability are derived.