Natural terrains composed of sands, soils, and other types of granular materials are subject to deformation and alteration when in uenced by interactions with humans and machines. These interactions include excavation and earthmoving activities such as digging, pushing, lifting, dumping, and piling. Simulating the deformation of sand and soil- lled terrains in interactive computer graphics applications is challenging due to the ne-grained and highly dynamic nature of these materials. In this thesis, we present the theoretical background, algorithms, and implementation details for a voxel-based terrain rendering system that simulates large, dynamic bodies of sands and soils in real-time 3D graphics applications. We describe a technique for representing soil in a 3D voxel grid, and we introduce a set of GPU-based algorithms that simulate the physical behaviors of soils in this representation. A multi-level height- eld is used to track the slopes of the soil-covered surfaces for slope stability analysis and soil slippage computations. The surfaces of the simulated soils are visualized each frame by extracting a polygonal mesh from the voxel grid with the Marching Cubes and Transvoxel algorithms. We show that our proposed algorithm is capable of producing realistic, high-quality simulations of soils with 3D e ects that are not possible in previous approaches. We also show that our proposed system is capable of operating in real-time on consumer level GPUs with over 60 frames rendered per second.