The long term behavior of the lining support in deep drifts is a crucial issue for nuclear waste underground repository project. In order to demonstrate the feasibility of the project, the French Radioactive Waste Management Agency (Andra) has built an Underground Research Laboratory (URL) at Bure. The underground structure is composed of a network of galleries whose drilling generates stress redistribution, damage and fracture in the surrounding medium. The damage and fracturing of this excavation damage zone have a direct effect on the displacement field and on the interaction between the formation and the lining support. The design of the support system request, in order to be as efficient as possible, a precise knowledge of the stress and displacement fields around the drift. For viscoplastic rock formation, the stress field around the drift and its effect on the support system must be determined for at least a couple hundred years. This is why we have studied the long term behavior of drifts using an elasto-viscoplastic constitutive law. The laboratory test data and field observations have shown that the Callovo-Oxfordian claystone has a slightly anisotropic behaviour for its elasticity, failure criterion and also creep properties. This anisotropy is largely increased by the presence of the fractures, which we take into account with transverse isotropic models. Homogenization techniques are used to establish a macroscopic expression of the viscous deformation depending on the behavior of the rock matrix and of the fractures. The macroscopic viscous deformation depends on the orientation and density of fractures, which is why based on investigation campaign, we divide the fractured zone, in our numerical models, into zones with fractures of different density and orientation to describe the behavior of the fractured zone as closely to the reality as possible. The model is then applied to the simulation of the convergences of GCS drift. The so called GCS drift belong to the network of monitored drift of the URL and was excavated in the direction of the major principal horizontal stress.