In this dissertation, an analysis procedure was established for the drilling and casing cementing process in salt wellbores, which encompasses cement hardening as well as salt creep. The objective of this dissertation is to analyze the geomechanical behavior of salt creep before, during and after drilling as well as the wellbore casing cementing process. Thus, the purpose of this study is to evaluate stresses and displacements around the wellbore through computational simulation with the finite element commercial software program Abaqus together with FORTRAN sub-routines. This analysis intends to understand the geomechanical effects of the interaction of the drilling fluid and slurry pressures against the wellbore and the behavior of the stress interactions between the two existing boundaries casing-cement and cement-salt formation; thus avoiding unnecessary workover operations that provoke economical losses. Diverse process simulations were performed including: (i) in situ stresses prior to drilling (ii) induced stresses due to drilling and salt creep and (iii) wellbore cementing. In these simulations, a 2D plane strain wellbore was considered. The drilling fluid was assumed to be non-penetrable with respect to the wellbore formation. Finally, the results were expressed in terms of radial displacement along with radial and tangential stresses.