This paper deals with a general variational approach to optimal control design for a class of hybrid mechanical systems. We study a special structure of the optimal control problems (OCPs) in the classic mechanics and apply the multiobjective optimization techniques in the solution procedure. The main dynamic model under consideration is given in the form of a nonlinear hybrid control system and incorporates the conventional two points boundary-value problems for the Euler-Lagrange or Hamilton equations. We consider the first order optimality conditions for OCPs governed by hybrid mechanical systems and also discuss some conceptual computational algorithms.