Summary: It has long been established that conforming algorithm approaches in BEM are reliable and robust for solving contact problems behaving under the hypothesis of small displacements and in the presence of initially conforming meshes. Non-conforming algorithm approaches have traditionally been associated with the presence of non-conforming meshes or with initially conforming meshes but in the presence of large displacements that alter the conformity of the meshes. In this paper, studying the Iosipescu test used to determine shear properties in composite materials, it has been shown that even in the presence of initial conforming meshes under the hypothesis of small displacements, the use of conforming algorithms leads to non-acceptable results, with incompatibilities in the displacement solution and with peaks in the distribution of the contact stresses. Several options to define the direction in which to establish the contact conditions were tested, all of them presenting problems. By contrast, the use of a non-conforming algorithm based on a weak application of the contact conditions previously developed by the authors reduces the incompatibilities and produces a smooth distribution of the contact stresses.