The structural simulation of parts under load to obtain information about the deformation and stress situation is a state-of-the-art approach. Simulation of flow is often performed as well. Combining both types of simulation to get an interaction between the flow and the structure is challenging due to the demanding requirements on the simulation software and computer hardware. Moreover, such simulations take a very long time to compute. This paper describes a coupled 3D simulation of the elastomeric parts and the flow in a diaphragm pump. A model of a diaphragm pump with the head assembly including the flow channels, the valves and the diaphragm is prepared for simulation in a structure and flow pre-processor. In addition, a coupling between the two approaches is defined. In the structural part, a nonlinear viscoelastic material model is used to describe the elastomeric parts such as the valves and the diaphragm. A compressible gas with heat transfer is used in the flow domain. The results show very good agreement with the valve displacement measured by a high speed laser Doppler vibrometer and the pressure in the working chamber measured by an ultra fast pressure transmitter. The valves open in their third eigenmode and oscillate at their third characteristic frequency. With this simulation method, it is possible to evaluate the functionality of different designs of the elastomer parts in the diaphragm pump considering the influence of the gas. Further relevant details about the flow behaviour in the diaphragm pump like the temperature rise due to gas compression and the associated heat transfer were obtained.