Abstract: Dynamic response of the MDOF nonlinear vibration system with uncertain parameters is studied. Based on interval mathematic, modeling the uncertain parameters as interval numbers, a new method, which approximately estimates the nonlinear dynamic response range with the help of first-order Taylor series, is presented. Comparisons between the interval analysis method and the probability perturbation finite element method in mathematical proof and numerical examples are performed, which show the advantages of the presented method, including less prior information need on uncertain parameters and higher accuracy.