In this paper, the mass optimization of four bar linkages is carried out using genetic algorithms (GA) with single and dual constraints. The single constraint of bending stress and the dual constraints of bending and buckling stresses are imposed. From the movement response of the bar linkage mechanism, the analysis of the mechanism is developed using the combination of kinematics, kinetics, and finite element analysis (FEA). A penalty-based transformation technique is used to convert the constrained problem into an unconstrained one. Lastly, a detailed comparison on the effect of single constraint and of dual constraints is presented.