In this paper, we focused on the advancement of Dam Monitoring Software that incorporates the Finite Element Method (FEM), as these large infrastructure constructions are crucial for ensuring a dependable water supply, irrigation, flood control, renewable electric energy generation, and safe operation, which is of utmost importance to any country. However, the material properties and geotechnical environments of dams can change (deteriorate) over time, while the standards and legal norms that govern them become more and more rigorous, so in order to accurately assess the state of a dam and detect any concerning behavior, the software must be updated as well. The custom-developed FEM solver, unlike many commercial alternatives, is adaptable and can be reconfigured to function within a Dam Monitoring System. In this paper, we present the procedure for interpolating numerical values at measurement points, when the position of the measurement point does not align with the node of the element, allowing for additional instrument locations to be added to the monitored system without the need for remeshing the numerical model. This procedure is used to compare the actual pore pressures and temperature values of the concrete dam structure with the prediction of the numerical model, and the agreement is much greater with the new interpolation algorithm in comparison to the nearest nodal values, with the average relative difference for pore pressure reduced from 8.89% to 8.10%, justifying this implementation.