A methodology is presented for the optimum design of high-speed multibody systems under time-dependent stress and displacement constraints by mathematical programming. Finite elements are used in the modeling of the flexible links. The design variables are the sectional properties of the elements. The time dependence of the constraints is removed through the use oi equivalent constraints based on the most critical constraints. It is shown that this approach yields a better design than using equivalent constraints obtained by the Kresselmeier-Steinhauser function. An optimizer based on sequential quadratic programming is used and the design sensitivities are evaluated by overall finite differences. The dynamical equations contain the nonlinear interactions between the rigid and elastic degrees-of-freedom. To illustrate the procedure, a Peaucellier-Lipkin mechanism is optimized by using different equivalent constraints.