A method for generating a three-dimensional geomechanical model of a subsurface volume is provided. The geomechanical model may be used to predict changes in geomechanical stress in the grid (such as a three-dimensional unstructured grid), which may be caused by extraction from or injection into the reservoir. The geomechanical model may be generated by solving, in combination, the finite element method at the vertices of a respective cell in the grid for momentum balance and the finite volume method at the center of the respective cell for mass balance. In this way, one or both of rock displacement or pore flow may be solved using the geomechanical model.