A complete analytical solution is presented for the linear diffraction of oblique waves by horizontal rectangular cylinders either fixed at the free surface or mounted on the sea bed in a finite-depth of water. Helmholtz equation is employed as the governing differential equation obtained by reducing the 3-D oblique wave scattering problem to a 2-D case. According to the method proposed, the fluid region is divided into three sub-regions in which the governing differential equation is solved by the separation of variables. The solutions for each region are then matched on the common boundaries, of sub-regions to determine the unknowns of the eigen series expansions and Fourier series. Thus transmitted and reflected waves are obtained in the far-field, and forces and moments acting on the rectangular cylinder fixed at the free surface are also given. Comparisons are made in order to check the accuracy of the method. (C) 2004 Elsevier Ltd. All rights reserved.