A method to model the nonlinear behavior of bridges using a grillage discretization is proposed. A modified stiffness matrix is used to account for material nonlinearity. The method accounts for material nonlinearities due to bending and shearing stresses. A program is developed to perform an incremental analysis of bridges subjected to vehicular loads. The validity of the model and program is verified by comparing to the results of full-scale field tests and published analytical results.