The present work deals with the generation of numerical grids for the appendages of a ship. A new method that follows the overlapping grid block approach is presented. For each block a structured 3-D mesh is generated, consisting of two-parametric grids that when projected on a planar surface form a curvilinear orthogonal 2-D grid. The presented method can model the appendages of a ship with twin propeller shafts, each having one or two I or V-brackets and twin rudder. The representation of the appendages is done parametrically and the method can deal with an extensive range of shapes and geometrical characteristics. Two example applications of the method are presented. The first is for a twin screw vessel with a single V-bracket per shaft and twin rudders. The second example regards a twin screw vessel with both an I-bracket and a V-bracket per shaft, bracket bossings that are faired with the shaft cover and twin rudders.