This article is devoted to the study of the local contact between the drillstring and the well during drilling operations. The study focuses on the Bottom-Hole-Assembly (BHA), which is subjected to compression. The work is motivated by the need to understand the complex behavior of such a system, in order to improve control over their constructive and destructive potentials. The contact zone is first determined using a global finite-element model obtained from a specific computer program. Contact, which is assumed to be located somewhere on the drill-collar or on stabilizers, is prejudicial and leads to premature abrasive wear of the drillstring, reduction of the Rate Of Penetration (ROP) of the tool into the rock and reduction of the Mean Time Between Failure (MTBF). The proposed mathematical model is expressed in terms of four independent degrees of freedom which are radial displacement, rotation of the section considered, bending along the tangential direction and torsion of the string. They include the effects of bending and torsion, the whirling motion of the drillstring as well as friction phenomena occurring between the drillstring and the well. The tangential effect is modeled by using Coulomb’s law of friction. The nonlinear equations of movement are derived using Lagrange equations and are solved numerically to obtain the response. Specific attention is paid to the study of friction and a consistent contact model capable of taking into account the rolling of the drillstring, both with and without slip, is included in the model. This paper also presents a parametric study on the influence of the initial position of the string and the friction coefficient of the contact on the dynamic behavior of the structure. The model is validated by an experimental set-up equipped with two opto-electronic devices.