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The mass sensitivity of the piezoelectric surface acoustic wave (SAW) sensors is an important factor in the selection of the best gravimetric sensors for different applications. To determine this value without facing the practical problems and the long theoretical calculation time, we have shown that the mass sensitivity of SAW sensors can be calculated by a simple three-dimensional (3-D) finite-element analysis (FEA) using a commercial finite-element platform. The FEA data are used to calculate the wave propagation speed, surface particle displacements, and wave energy distribution on different cuts of various piezoelectric materials. The results are used to provide a simple method for evaluation of their mass sensitivities. Meanwhile, to calculate more accurate results from FEA data, surface and bulk wave reflection problems are considered in the analyses. In this research, different cuts of lithium niobate, quartz, lithium tantalate, and langasite piezoelectric materials are applied to investigate their acoustic wave properties. Our analyses results for these materials have a good agreement with other researchers' results. Also, the mass sensitivity value for the novel cut of langasite was calculated through these analyses. It was found that its mass sensitivity is higher than that of the conventional Rayleigh mode quartz sensor.