The main purpose of casing cementing is to assure zonal isolation and borehole integrity. The aim of this paper is to describe the elements associated with borehole integrity in salt zones. To achieve this, a numerical analysis of the contacts amongst the rock salt, cement and casing was carried out using the finite element method. The problem was divided into two parts. The first part focuses on a step-by-step procedure from drilling to cementing. The second part considers the long-term response of the wellbore after cementing. This paper focuses on the drilling of the wellbore and on the hardening of the cement. The casing was simulated as a metallic, plastic material w ith a von Mises yield surface with associated plastic flow. The cement was simulated first as an elastic material with a step-by-step strengthening gain and then in the last step as a plastic frictional material with a linear Drucker-Prager yield surface. Finally, the time, stress, temperature dependent behavior of rock salt was defined as a secondary or steady state double mechanism crccp law. A non-linear, 3D finite element (FE) commercial program was chosen (ABAQUS), and some subroutines were created (FORTRAN) to develop the creep law. The paper also discusses issues such as salt in-situ stresses, induced stresses by the drilling fluid and slurry, and cement hardening processes. Developments of stresses through the different steps were analyzed and contact between these three different materials (salt, casing and cement) were also studied The main contribution of this research is determining the effect of salt creep and contacts amongst the materials before, during and after drilling the well.