Static non-linear Hamilton-Jacobi equations are often used to describe a propagating front. Advanced numerical algorithms are needed to effi- ciently compute solutions to these non-linear equations. In geological modelling, layers of rocks can be described as the position of a propa- gating front at different times. A fast simulation of such layers is a key component in exploration software developed by Kalkulo AS for Statoil AS. Developing fast algorithms and solvers is essential in this application, since faster solvers enables users to test more geological scenarios, leading to a better understanding of the inner earth. Front propagation is also used in other applications, such as reservoir simulation, seismic processing and medical imaging, making a fast algorithm highly versatile.The recent years rise of parallel architectures has made substantial computational resources available. One way to originate faster solvers is therefore to develop algorithms that are able to exploit the increasing parallelism that these architectures offer. In this thesis, a novel three- dimensional anisotropic front propagation algorithm for simulation of geological folds on parallel architecture is presented. The algorithm’s abundant parallelism is demonstrated on multi-core CPUs and GPU architectures. Implementation on multi-core architectures is achieved by using the OpenMP API, while the Mint programming model is used to facilitate with the GPU programming.We demonstrate 7x to 2x speedups running on the Nvidia GeForce GTX 590 GPU, compared with a multi-threaded implementation on a NUMA- machine using two interconnected 12 core AMD Opteron processors. These results point to enormous potential performance advances of our algorithm on parallel architectures.