In this paper, hybrid metaheuristic optimization algorithms are used for the dynamic synthesis of a flexible four bar mechanism. The design variables vector including, lengths, widths and thicknesses of the four bars, and the material characteristics’ such as the Young modulus and material density, is identified based on the mechanism dynamic responses. Different dynamic responses are considered, such as the coupler and the follower mid-point transversal deflections and trajectories. A mono-objective and multi-objectives hybrid optimization synthesis combining PSO, DE and JAYA algorithms based on these responses taken separately and all together have been presented. The optimization efficiency has been proved through numerical simulations carried on MATLAB software.