We present recent developments in the Discrete Element method (DEM) for analysis of drilling mechanics problems typical in the oil and gas industry. A new local DEM constitutive model able to predict the non-linear behavior of soft and hard soils and rock under loads inducing multi-fracture of the material is presented. The DEM model is validated on the analysis of triaxial tests on cement and concrete samples and then applied to the study of drill-bit mechanics. Applications of the DEM and a combined DEM-FEM procedure to drilling problems are presented.