Orthotropic plates form an essential part of many marine, aerospace, and automobile structures. The recent increase in the use of composite materials for plate-type structures intensified the need for solutions utilizing orthotropic plates. These structural components, in many instances, are subjected to vibration. The main purpose of this paper is to present a semi-analytical analysis of the response of orthotropic plates to forced vibrations with different combinations of boundary conditions subjected to a general distributed excitation. The solution of the partial differential equation was reduced to an iterative sequential solution of ordinary differential equations using extended Kantorovich method. The efficiency and accuracy of the proposed method were examined through comparison with available literature and was in good agreement with them.