Simulation of wave propagation in the three-dimensional (3D) modeling of the vocal tract has shown significant promise for enhancing the accuracy of speech production. Recent 3D waveguide models of the vocal tract have been designed for better accuracy but require a lot of computational tasks. A high computational cost in these models leads to novel work in reducing the computational cost while retaining accuracy and performance. In the current work, we divide the geometry of the vocal tract into four equal symmetric parts with the introduction of two axial perpendicular planes, and the simulation is performed on only one part. A novel strategy is defined to implement symmetric conditions in the mesh. The complete standard 3D digital waveguide model is assumed as a benchmark model. The proposed model is compared with the benchmark model in terms of formant frequencies and efficiency. For the demonstration, the vowels /O/, /i/, /E/, /A/, and /u/ have been selected for the simulations. According to the results, the benchmark and current models are nearly identical in terms of frequency profiles and formant frequencies. Still the current model is three times more effective than the benchmark model.