<p>This paper presents an innovative formulation of the finite element method employed in the nonlinear analysis of membrane structures. The formulation developed has a total Lagrangian feature and is based directly on nodal positions instead of displacements, leading to a geometrically exact description in a simple and straightforward way. Therefore, large deflections are naturally considered. The membrane positional element proposed here has a pseudo-solid kinematic, resulting in a square and invertible mappings in the calculation of the deformation gradient and allowing to consider constitutive models that presents volumetric changes in the elastic phase. The prestress state is applied using a prestress gradient to relate the reference configuration to an undeformed one. Solid elements are used to compare with membrane results and cable elements are also considered in the model, also using the positional approach. Numerical examples are presented to illustrate the robustness and effectiveness of the formulation.</p>