We have developed a model to simulate the formation and evolution of hydraulic fractures. The model relies on a discrete spring network representation of the fracturing media and a continuum description of the fluid pressure that diffuses within it. The model is both versatile and efficient due to the lack of redundant components in the description of the fluid dynamics and the simple mechanics of the spring network. The model is validated quantitatively in a simple test case where it is shown that the pressure forces on the solid agree with theoretical predictions. Subsequently, it is applied to some simplified geological scenarios in order to explore some generic effects. While no attempt has been made to apply representative parameters for real geological systems, the model demonstrates that the fracture formation depends crucially on the way pressure diffuses into the rock, both in the case of a point pressure source and in the case of a sandwich or caprock geometry where high fluid pressure causes hydraulic fracturing of a low-permeability lid layer. Finally, the continuum limit of the elastic system is obtained analytically in order to identify the proper macroscopic parameters that are needed when simulations are to be matched to real geological systems.