The article introduces a novel integrated moving element method (IMEM) to hydroelastic analysis of infinitely extended floating plates under moving loads in shallow water conditions. The floating plate is modeled via the Kirchhoff-Love theory, while the linearized shallow-water equation is adopted for the hydrodynamic modeling. Both computational domains of fluid and structure are concurrently discretized into “moving elements” whose coordinate system moves along with applied loads. Accordingly, the paradigm can absolutely eradicate the update procedure of force vector owing to the change of contact point with discretized elements not only for the plate but also for the fluid. Furthermore, the IMEM also requires fewer number of discrete elements than the standard finite element method (FEM) due to their independence with the distance of moving load. Results obtained in several numerical examples are compared with those of the Fourier Transform Method (FTM) to validate the accuracy and effectiveness of the proposed methodology. In addition, the influence of water depth, load speed, multiple contact points, as well as the distance between axles on the dynamic amplification factor of plate displacement and the loading's critical speed is also examined in great detail.