We present a novel method for 3D anisotropic front propagation and apply it to the simulation of geological folding. The new iterative algorithm has a simple structure and abundant parallelism, and is easily adapted to multithreaded architectures using OpenMP. Moreover, we have used the automated C-to-CUDA source code translator, Mint, to achieve greatly enhanced computing speed on GPUs. Both OpenMP and CUDA implementations have been tested and benchmarked on several examples of 3D geological folding.