Contact between beam elements in a finite element model usually is done with special techniques, taking advantage of the beam axis description. Physically, contact takes place on external surfaces of beams but, when the cross section is circular or tubular, geometric simplifications can be made, creating simpler contact descriptions. In this context, we may introduce the master-master technique, in which two convective coordinates are chosen to describe the material points, contact-candidates. Contact is assumed pointwise and acting at material points of both curves, determined by the so-called “orthogonality relations”. Such material points may change along the model evolution, which permits the establishment of a moving pointwise action by a single contact pair model.