<p>Decreasing the computational cost has always been a challenge for engineers. One well-known approach is to employ a model with appropriate performance that allows for using a lower number of elements. Another approach is to use transition elements over the geometry, which enables mesh refinement in an area of interest. This study introduces two novel finite elements tailored for membrane analysis with improved computational efficiency and accuracy. The first element is a five-node quadrilateral membrane element called USQ5, which uses the unsymmetric finite element method (UFEM). This method performs well in problems involving complex geometries and boundary conditions. The element’s test function is a displacement field enriched with rotational degrees of freedom at each node, and the trial function is a stress field formulated based on analytical stress solutions. Using a similar method, a six-node triangular membrane element, named UST6, is proposed, formulated by applying UFEM principles. The scientific contributions of this work lie in the novel application of UFEM to improve solution accuracy while reducing the number of required elements. Results obtained from numerical benchmark problems show that both the proposed USQ5 and UST6 elements exhibit reasonable accuracy and a good convergence rate. The maximum errors for the USQ5 and UST6 elements are 0.6 and 0.5%, respectively. These results demonstrate the effectiveness and potential of the proposed elements in handling complex structural problems with high efficiency.</p>