A method is presented for computing the nonlinear dynamic response of planar cable-stiffened structures. The nonlinear dynamic equations are reduced to a smaller system by expanding the unknown variables as a series of mode shapes which were found by an eigenvalue analysis of the linear dynamic equations. The method is applied to two types of cable-stayed bridges. Results are presented for the static, linear dynamic, and nonlinear dynamic responses of these structures. The effect of damping is also indicated in the computations. It is found that for the structures under investigation a linear dynamic analysis is suitable.