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Seismic modeling in anisotropic media is computationally intensive, necessitating efficient numerical strategies to meet modern survey demands. This study investigates half-precision (FP16) arithmetic to accelerate 3D elastic wave propagation in elastic anisotropic media. We employed GPU-accelerated finite-difference time-domain (FDTD) method on staggered grids to optimize the 3D elastic wave equation, ensuring numerical stability in FP16 arithmetic. The results demonstrate that FP16 arithmetic reduces the overall computational overhead while preserving sufficient numerical accuracy for resource-intensive applications such as full-waveform inversion (FWI) and reverse time migration (RTM). Future work will validate the framework across diverse anisotropic models and explore adjoint-based FWI and BF16 formats. By leveraging mixed-precision computing and modern hardware, this approach offers a scalable solution for large-scale seismic modeling, balancing efficiency and accuracy for geophysical exploration.