This study introduces the Finite Web Method (FWM), a novel mesh-based Generalized Finite Difference Method (GFDM) designed for seamless integration with triangular meshes in the Finite Element Method (FEM). By utilizing web-shaped configurations around central nodes, FWM ensures consistent satisfaction of the four-quadrant criteria for node placement. Its computational performance is evaluated through a 2D screw plate tension simulation and validated against FEM results using quadratic triangular elements. Two node arrangement strategies, linear and quadratic triangular element-based distributions are analyzed under varying mesh sizes. The results show strong agreement between FWM and FEM in predicting stress and displacement fields. The linear approach, while underestimating results due to fewer nodes and scattered distributions, improves in accuracy with higher mesh densities. In contrast, the quadratic approach demonstrates superior accuracy and computational efficiency, surpassing the linear approach when the number of nodes exceeds a certain threshold. Convergence analysis highlights the importance of node distribution, with the quadratic approach achieving a higher convergence order. These findings underscore FWM’s versatility and efficiency in simulations with different triangular mesh configurations.