Generally a piping system and other machine structure system such as a crane and a boiler attached to a building or the ground are subjected to more than one seismic motions directly or indirectly. In this paper attention is focused on this fact and equations of a simple proposed building-machine structure system which is simulated as a lumped mass system are set up and its response characteristics are investigated by the analog computer. The equations of motion for both systems are written in a relative displacement form for each boundary and these are connected with each other by reaction terms. From the results of these response analyses it is concluded that the coincidence of both structure periods is in the worst condition and that the damping and mass ratio of a machine system to a building gives serious influence on the response amplification especially in the neighboring region of resonance. Finally, a simple method of the response analysis for a machine system is proposed and discussed.