An analytical and numerical analysis of fluid filled crack propagation in three dimensions Fluids in the Earths crust can move by creating and flowing through fractures in a process called `hydraulic fracturing’. The tip line of such fluid filled fractures grows at locations where stress is larger than the strength of the rock. Where the tip stress vanishes the fracture closes and the fluid front retreats. If stress gradients exist on the fractures walls induced by fluid rock density contrasts or topographic stresses this results in an asymmetric shape and growth of the fracture allowing for the contained batch of fluid to propagate through the crust. The state of the art analytical and numerical methods to simulate fluid filled fracture propagation are two dimensional (2D). In this work I extend these to three dimensions (3D). In my analytical method I approximate the propagating 3D fracture as a penny shaped crack that is influenced by both an internal pressure and stress gradients. In addition I develop a numerical method to model propagation where curved fractures can be simulated as a mesh of triangular ...