For floating plates, it is important to remain the stability of the plates which float on water surface. Previous studies have mentioned many different methods to alleviate vibrations of the plates. Using anchors to remain the plates stable is one of those methods. Previous studies have mentioned a lot about the effect of elastic anchors on sheets. However, in these studies, floating plates are often considered as a line element and have yet considered the plate with an elastic anchor system. Based on these studies, a floating plate subjected moving loads with elastic connections to the seabed is considered dynamic behaviors. In this study, the combination of Boundary Element Method (BEM) and Finite Element Method (FEM) is used to simulate the behaviors of floating plate in consideration of the elastic mooring lines. The influence of elastic mooring lines on the displacement and oscillation of the plate is studied based on numerical investigations.