A mathematical model for the in-plane dynamic analysis of motorcycles is presented and the performance during an emergency braking manoeuvre is analysed. The effects of braking torque amplitude and time constant are discussed and the problems of lock-up and loss of contact of the rear wheel are highlighted. The suspensions' vibrations during braking are analysed by means of modal analysis. An optimisation method is developed in order to find the braking torque and the suspension parameters that minimise the stopping distance. The method takes the complete dynamic behaviour of the vehicle during braking into account and is based on a non-derivative minimisation algorithm. Several results are presented that show the possibility of shortening the stopping distance by optimum design of one or both of the suspensions.