Computational costs limit large scale reservoir simulations to coarse grid systems. Determination of an effective permeability for a simulation grid block requires a proper scale-up of small scale permeability heterogeneities within that grid block. Conventional scale-up techniques are limited to a diagonal tensor representation of effective permeability. Therefore, such techniques cannot handle general permeability anisotropy (full tensor) exemplified by cross-bedded permeability structures that may be present on a smaller scale. An analytical method is developed to calculate an effective permeability tensor for a grid block by accounting for small scale heterogeneities within the grid block. The method honors both the location and the orientation of the small scale heterogeneities. Effective permeability tensors calculated using the analytical method and a numerical method show excellent agreement. Miscible displacement simulations show that the effective permeability tensor method outperforms conventional scale-up techniques in predicting flood front locations in cases of general permeability anisotropy.