The present research was mainly motivated by petroleum geomechanics problems such as solids production and formation damage. Solids production is related to phenomena whereby solid particles are produced together with fluids from reservoir rocks having little or no consolidation although it is reported that those phenomena have already happened to more resistant materials. Formation damage is the term used in order to identify permeability reduction occurring for various processes and which reduce productivity and injectivity of wells in oil and gas production systems. In the present work, a numerical tool considering fluidmechanical coupling (one and two phase flow) was developed for analyses in the microscale (pores and grains). The DEM (Discrete Element Method) was used for the simulation of motion and interaction of solid particles and the lattice Boltzmann method (LBM) for the simulation of flow inside pores of the geological media. The main difference between the developed tool and the ones developed in previous works that couple DEM with LBM is the introduction of incompressible LBM as suggested by (He e Luo, 1997), one that allows the application of pressure gradients considerably larger than the conventional formulation which is important for the simulation of solids production. The developed tool can be viewed as a virtual laboratory for testing and verification of constitutive laws which together with experimental data may improve the understanding of basic phenomena involved in formation damage and solids production. The numerical implementation was verified through comparisons with analytical solutions and other results from the literature. Simulations related to practical applications were carried out and discussed.