During the injection of a fluid into a medium in order to displace another fluid, the interface may be unstable and finger shape patterns of displacing fluids are formed in the bulk of the displaced fluid. In this article, fingering in fractures and porous media is modeled using the "Shan-Chen-type Multicomponent Multiphase Lattice Boltzmann" method based on statistical mechanics. Results of the simulations are presented in terms of finger shape versus time, length of fingers, and the recovery versus dimensionless pore volume of displacing fluid injected into the media for different sets of capillary number and mobility ratios. Based on these investigations the proposed model is a promising tool to study displacement in complex geometries.