In this paper, a lattice type model is used to gain an insight into the constitutive behavior of granular media. In a two dimensional simulation, the grains in a granular medium are idealized as elastic discs. In the lattice type model, nodes are introduced at grain contacts and the nodes are linked by bars. An assembly of grains, represented as discs, is transformed into truss elements and the truss is then analyzed using matrix method of structural analysis. The areas of bars are derived by computing the displacements of an elastic disc under contact forces and then determining the bar areas that will give equivalent displacements in the direction of the bars. Bonding, debonding, sliding and rotation of particles as well as breakage of particles are incorporated in this model. The lattice type model is applied on a very loose packing and a very dense packing. The two packings are subjected to simple shear test conditions, simulated by applying an initial vertical load followed by a triangular variation of displacements for the nodes along the vertical boundaries. The results of the numerical tests are in general agreement with the behavior of sands in laboratory simple shear tests. The constitutive behavior of the granular media using the lattice type model and its potential to evolve the macro-behavior of granular media from the micro-structural properties are discussed.