In this study, an algorithm is designed specifically for automatic finite element (FE) mesh generation on the transverse structure of hulls reinforced by stiffeners. Stiffeners attached to the transverse structure are considered as line constraints in the geometry boundary. For the FE mesh generation used in this study, the line constraints are treated as boundaries and by that means the geometry domain attached to the line constraints is decomposed into sub-domains, constrained only by the closed boundaries. Then, the mesh can be generated directly on those sub-domains by the traditional approach. The performance of the proposed algorithm is evaluated and the quality of the generated mesh meets expectations.