In this paper, the free vibration of an undamped triple-beam system on elastic foundation is analysed. The system consists of three Euler-Bernoulli beams of the same length that are arranged in parallel and continuously connected by elastic layers. The natural frequencies and the mode shapes of the system are determined. Furthermore, the initial value problem is solved to find the time-dependent free vibrations of the beams. Using a numerical example, the effects of the layer stiffnesses and those of the masses of the beams per unit length on the natural frequencies and the mode shapes are investigated in detail.