This paper investigates the influence of cohesion on the behavior of 2D granular media simulated by using a molecular dynamics method, involving a simple contact law with adhesion. The study considers an adhesion index which is non intrinsic but significant for interpreting the mechanical effects of applied pressure. A static state system of 4000 particles is numerically simulated by oedometrical compression under a constant force, without gravity. The results show how the geometrical texture and the network of contact forces change according to the level of adhesion. This effect is explained essentially in term of the increase in the number of the tensile contacts and by the development of the internal self-stress structure. As in the case of non cohesive granular media, a high spatial heterogeneity of the contact forces is observed.