The patterns of the pressure and the flow velocity fields of the working fluid are discussed within this work for the different phases in the working process of multi-valve reciprocating compressors. The flow velocity field near the compressor walls can be used e.g. for the computation of a time and space dependent convective heat transfer coefficient in the context of a boundary layer description. For the automatically opening and closing suction and discharge valves only plate valves are considered. The dynamics of the plate lift has an important influence on the mass flows crossing the valves, and as a consequence on the flow inside the compressor's working chamber. Hence, the motion of a solid body affects the fluid flow. On the other hand, the gas pressure force acting on the valve plates is considered in the equation of motion based on a mass-spring-model. Therefore, we have a simple form of a fluid-structure-interaction (FSI). For finding the approximate solution of the flow field, a self-developed code in the programming language C is used for the time-dependent three-dimensional Euler-equations. Assuming ideal gas as the working medium, the conservation equations for mass, momentum and total inner energy are solved numerically neglecting the fluid viscosity and the heat flows. In order to solve the time-change of the quantities, the finite-volume-method based on a first-order accurate time-integration scheme is used, where the numerical fluxes at cell boundaries are computed with the approximate Riemann-solver of Roe. With this method, it is possible to handle subsonic and supersonic flows, as well. A challenge in the computation of the flow is the moving computation-mesh caused by the piston, and the geometrically difficult zone connecting the cylinder and the valves, the so-called valve-pockets. Because of this motion, a structured hexahedral mesh is used for the cylinder while for the valve pockets a tetrahedral mesh is considered, that can partially be covered by the piston. Cylinder mesh and valve pocket meshes are finally connected by an interface routine that fulfills the requirements of conservation. Hence, it is guaranteed in the case of closed valves, the total mass contained inside the cylinder and the valve pockets remains constant.