The X-Mesh method, introduced in [1] and applied to Stefan problem, is a versatile approach for handling complex interface problems. The method was then applied to material interfaces in [2] with the simulation of two-phase flows with surface tension. In this work, we further extend the application of X-Mesh to a new class of material interfaces: fluid-structure interactions (FSI). In this method a deforming mesh with fixed topology and continuous movements of nodes permanently match the interfaces of interest, even in the case of topological changes of the fluid domains. To achieve this goal the method authorises zero-measure elements, meaning a triangle can deform to an edge or even a point. This allows the mesh to deform in a time continuous manner and provides the relaying of the front. The interface is transferred from one node to another node located at the same position enabling interface propagation. Those degenerated elements are handled robustly using the Tempered Finite Element Method (TFEM) [3]. This approach draws inspiration from Arbitrary Lagrangian-Eulerian (ALE) formulations but addresses some of their key limitations. Specifically, X-Mesh eliminates the need for remeshing the domain when interfaces undergo large displacements and it avoids numerical diffusion associated with solution projection onto a new mesh. The proposed methodology is validated through simulations involving interactions between incompressible fluids and both rigid and flexible structures. Results demonstrate the capability of X-Mesh to accurately capture the dynamics of FSI scenarios while maintaining numerical stability and solution fidelity.