The focus of this research was to formulate optimization model of 16-bar trussesalong with stress, stability and deflection constraints. The derivative free methods were used for theoptimization of engineering design problems. These methods were basically designed forunconstrained optimization problems. In formulated optimization truss problems the constraints werehandled by using exterior penalty functions. The results of the truss optimization model were obtainedby using MATLAB which demonstrated the effectiveness and applicability of these derivative freemethods. It was concluded that the results of Nelder-Mead method were not acceptable due to their faraway convergence even its number of function evaluations were smaller than number of functionevaluations of Multi-Directional Search method and Hooke and Jeeves method. By comparing theoptimal function values obtained by these three methods, the performance of Hooke-Jeeves methodwas better than the other two methods.