This paper presents the analyze of the stress distribution in the neighborhood of a horizontally mining excavation with either a circular, or a non-circular transverse cross-section (a square with rounded corners). The displacement field using the non-associated elasto-viscoplastic model, with a viscoplastic potential, is also given and compared with the "in situ" displacement field measurements. The analyze of these results, as compared with the theoretical ones, show a good matching. Thus the constitutive equations determinated for rock salt is able to capture the main feature of this rock, and can well be used in underground design.