In reservoir simulations, one of the biggest challenges is solving large modelswith complex geological properties. Because reservoirs can be several kilome-ters long, and still be geologically inhomogeneous over centimeters, the com-putational power required to solve a full set of mass balance equations can beimmense. Several methods for overcoming this challenge has been proposed,including various upscaling and multiscale methods.One of these approaches is the Multiscale Finite Volume (MsFV) method, whichaims to create a set of basis functions for the pressure which can be computedin parallel and reused for different boundary conditions. This thesis aims togive a thorough study of the MsFV-method itself, before extending it to threedimensional, unstructured grids. An implementation was done as a modulefor the MATLAB Reservoir Simulation Toolbox developed by SINTEF AppliedMathematics. A new variant of the method designed to overcome some of thecomputational challenges arising from an extension to 3D was also formulated.The implementation was then applied to both synthetic and realistic gridsand permeabilities, and compared against a full two point flux approximation(TPFA) solver.