Abstract: A new algorithm for dynamic elastoplastic analysis is put forward on the basis of parametric quadratic programming and exact integration. The equations of dynamic elastoplastic problems are derived from the parametric variational principle and parametric quadratic programming, being valid for both associated and non-associated plastic constitutive models in finite element analysis. Exact integration method, which has been widely used in linear problems, is adopted for the solution of dynamic nonlinear equations. A numerical example is provided to demonstrate the correctness and the advantage of the proposed theory and algorithm.