Featured with a higher velocity, increased power handling capability, and better aging behavior, surface transverse wave (STW) shows more promising prospects than Rayleigh wave nowadays in various sensing applications. The need to design, optimize, and fabricate the related devices motivates the development of modeling and simulation. For this reason, a three-dimensional (3D) finite element (FE) simulation of STW on quartz, considering the crystal cut angle and the electrode effects, is presented in this study. Firstly, we investigated the effects of quartz’s cut angle on the generated waves. Here, the polarized displacements were analyzed to distinguish the wave modes. Secondly, the investigations of the electrode effects on the polarized displacement, phase velocity, and electromechanical coupling factor ( K²) were carried out, for which different material and thickness configurations for the electrodes were considered. Thirdly, to examine the excitation conditions of the generated waves, the admittance responses were inspected. The results showed that not only the crystal cut angle but also the density and the acoustic impedance of the interdigital transducer (IDT) material have a strong influence on the excited waves. This article is the first to analyze STWs considering quartz’s cut angle and electrode effect through a 3D FE model. It could provide a helpful and easy way to design, optimize, and fabricate the related surface acoustic wave devices.