This paper describes the typical finite element methods and the variational principles for two elastic contact bodies. The following results are obtained in this paper : (1) The two-dimensional behavior for the longitudinal impact of two uniform rods is calculated, using the tinite element method for elastoimpact contact structures. An impact contact force is decomposed into a stationary component due to contact displacement and a variable component due to contact acceleration. The variable component is within the range of a maximum ±10.4 %. Therefore, the impact force can be approximately expressed by the stationary component. (2) The stationary component of the impact force corresponds to a Lagrange multiplier in the variational principle. An approximate hybrid type of virtual work principle is formulated in various contact and separate states of two bodies. If the components of velocities and accelerations are eliminated in this principle, a precise virtual work principle for static contact structures can be derived. Using the concept of relative movement, the matrices degree of the finite element method based on this principle remains constant in various contact and separate states.