The polynomial type Lagrange equation and Hamilton equation of finite dimensional constrained dynamics were considered. A newalgorithm was presented for solving constraints based on Wu elimination method. The new algorithm does not need to calculate the rank of Hessian matrix and determine the linear dependence of equations,so the steps of calculation decrease greatly. In addition, the expanding of expression occurring in the computing process is smaller. Using the symbolic computation software platform, the new algorithm can be executed in computers.