This paper presents the hydroelastic vibration analysis of clamped rectangular plates, vertically or horizontally submerged in fluid by using isogeometric finite element and boundary element methods. The method of analysis is divided into two parts. In the first part, the dynamic characteristics of the structure, in vacuo conditions and in the absence of external forces, are obtained by NURBS-based isogeometric finite element method (IGAFEM). In the second part of the analysis, the fluid-structure interaction effects are calculated by using a NURBS-based isogeometric boundary element method (IGABEM) in conjunction with the method of images, in order to impose appropriate boundary condition on the fluid's free surface. By adopting the linear hydroelasticity theory, the fluid is assumed ideal, i.e., inviscid, incompressible and its motion is irrotational. The fluid-structure interaction effects are calculated in terms of the generalized added mass coefficients. In order to demonstrate the applicability of the proposed method, two different clamped rectangular plates were adopted for the calculations. The effects of the plate thickness and aspect ratio are also investigated. The predictions compare well with available numerical and experimental results found in the literature.