So far, mathematical modelling of Lamb wave propagation under fluid-structure interaction (FSI) was limited to the case of rigid structure. We extend this concept to account for structural dynamics. Thereby, we provide a model that is suitable for the structural health monitoring (SHM) during the operation of the structure. The model we develop is referred to as the “eXtended Fluid-Structure Interaction” (eXFSI) problem, which is a one-directional coupling of typical FSI problem with an ultrasonic wave propagation in fluid-solid and their interface (WpFSI). Here, the strongly coupled problem of acoustic & elastic wave equations is denoted by WpFSI. Next, we explore the approach to the efficient numerical solution of the problem. We use a combination of Finite Element and Finite Difference methods and employ a dual-loop algorithm to balance the computational cost and quality of the numerical solution. To facilitate our solution algorithm, we rely upon the software library package DOpElib.

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