A new efficient system identification method is introduced to determine the model structure and parameter estimates of an unknown structural system to produce a multi-input multi-output (MIMO) model. No a priori knowledge is assumed regarding the nonlinearities. When the system involves lumped masses, all the information about the locations, types, and coefficients of both linear and nonlinear links which connect the lumped masses in the system can be determined in one efficient procedure. The new algorithm yields a parsimonious continuous time model which is useful for the interpretation of the system in practical applications. An illustrative example demonstrates the efficiency of the new method.