Models of mechanical systems often contain unknown system parameters which cannot be determined directly from component tests. System identification techniques are methods which determine the unknown parameters based on the overall system behavior under prescribed dynamic loading. In this work a methodology was developed for identifying the unknown parameters in a nonlinear mechanical system model which produces a high degree of correlation between the model response and the test data. This technique uses numerical optimization algorithms to minimize differences between the model response and the test data. Two algorithms are used: the BFGS quasi-Newton method and the zero-th order POLYTOPE method. Several example problems are solved which demonstrate our methodology. Both methods accurately identify the unknown parameters in simple mass-spring-damper systems. For more complex nonlinear systems, such as the occupant simulation models, the gradient-based BFGS method is unable to identify the correct parameters in two test cases. This is due to the fact that the objective function contains many local minima for these systems. The POLYTOPE method gives satisfactory results for identifying complex nonlinear systems in all three test cases investigated in this study. For complex nonlinear systems the form of the objective function can affect the final solution. Best results will be achieved when the objective function is highly sensitive to the changes of the unknown parameters.