The present paper describes a set of procedures for the solution of nonlinear static-equilibrium problems in the complex multibody mechanical systems. To find the equilibrium position of the system, five optimization techniques are used to minimize the total potential energy of the system. Comparisons are made between these techniques. A computer program is developed to evaluate the equality constraints and objective function of a general multi-body dynamic system in order to find the equilibrium condition. The obtained results from different approaches are compared together and finally some conclusions are made considering the existing results of the artificial damping method. It is seen that the indirect methods may produce more accurate results with faster convergence.