Abstract: Wave scattering and hydroelastic response of semi-infinite elastic plates due to obliquely incident waves in a three-layer fluid are studied analytically. The densities of the three layers of fluid are different with sharp interfaces, but are constant at each layer. The fluid is assumed to be inviscid and incompressible and the motion to be irrotational. Within the frame of the linear potential flow, semi-analytical solutions for wave-plate interaction are derived with the aid of the methods of matched eigenfunction expansions and the inner product of eigenfunction. The critical angles for the incident waves of the surface mode and the interfacial wave mode are deduced in terms of the dispersion relation. As the physical parameters change, the critical angle varies accordingly. The critical angle are closely related with the existence of the surface or interfacial wave modes that propagate from the open water region to the plate-covered one, by which two problems can be answered: (1) Is there a transmitted wave on the incident interface in the plate-covered region; (2) Is there, on the interfaces above the incident surface, a transmitted wave on the plate-covered region and a reflected wave in the open water region. When the low interfacial wave is incident and the incident angle is large enough, the low interfacial wave mode in the open-water region becomes the solo wave mode in the entire fluid domain.