A novel method coupling computational fluid dynamics (CFD) and finite element method (FEM) was developed to account for the complex physics of the reciprocating compressor. The developed method is based on data exchange between the two solvers at each time step. We address the challenges related to valve dynamics, where the motion of solid components is not prescribed as for pistons, but result from the combined interactions between pressure, velocity, spring forces and impact forces during each revolution. The coupling method enables accurate computation of the solid-fluid interaction, where at each time step the pressure acting on the valve computed by CFD is transferred to the FEM simulation, and the three-dimensional valve motion computed by FEM is transferred to the CFD simulation. It is demonstrated on the dynamics of a ring plate discharge valve in a reciprocating ammonia compressor to quantify the effect of impact damping which arises from the gas dynamics, leading to reduced forces on the valve. The results from the coupling simulations are compared against novel experimental measurements obtained by instrumenting a real compressor. The coupled CFD-FEM simulation gives detailed insights into the valve behaviour and was used also to investigate pressure inhomogeneities, which can lead to tumbling motion of the valve ring.