Numerical analysis for valve train dynamics of an internal combustion engine is presented. The components of the valve train are modeled by finite element techniques, and the dynamic contacts between the components are analyzed by the solution strategies of differential algebraic equations. Also an iterative scheme similar to the augmented Lagrange multiplier method is employed to enforce the contact constraints. It is shown that the contact and separation between the components of the valve train can be computed by the finite element techniques, and the numerical examples are presented to demonstrate the efficiency of the solution.