In this report, the finite element method is applied to shells modeled using membrane and plate elements. The main objective of the work has been to evaluate the performance of in-plane 3-node membrane elements in an effort to establish if there is such a thing as a "best" membrane element. For this purpose, standard benchmarks problems are analysed. A 3-node, 9-dof membrane triangle with corner-drilling freedoms is implemented. The implementation is based on a parameterized variational principle presented by C.A. Felippa and co-workers. The theory formulates membrane templates containing several free parameters that can be set to replicate existing membrane elements. In order to get results of relevance for practical application, calculations have been performed for several finite element ship models.