In this paper is presented the optimal design of quarter car vehicle suspensions. During the optimisation the three design criteria which have been used are; vertical vehicle body acceleration, dynamic tire load and suspension working space. For implementing a optimization a comparison of two optimisation algorithms: Sequential Quadratic Program (SQP) and Genetic Algorithms (GAs). will be chosen five design parameters: sprung and un-sprung mass, spring stiffness, damping coefficient and tire stiffness. Through the simulation in Matlab it will be shown that GA is more powerful tool to find the global optimal point, without any restrictive requirements on the gradient and Hessian Matrix, while SQP has local convergence properties. The main focus of this research will be on minimising the vertical vehicle body acceleration subjected to a suspension working space and the dynamic tire load. At the end of this paper, it will be shown the comparison between the simulation carried out with nominal and optimal values of design parameters.