This article deals with the interaction between wave effects in mounts and resonances of foundations inflexible vibration isolation systems. A new model is proposed that is represented as a rigid mass supported by two linear unidirectional isolators on a flexible foundation beam, whose closed-form solutions for transmissibility and response ratio are then obtained, with which the influence of wave effects coupled with the flexibility of the foundation on the effectiveness of isolation is discussed. The wave effects on flexible isolation systems are analyzed under various parametric conditions and compared with those in rigid systems. In addition, several special cases are presented to show the transition between various limiting cases. Some approaches to control wave effects are also proposed.