The success rate of reconstructing the Anterior Cruciate Ligament (ACL) with prosthetic ligaments is currently low both in humans and animals. The stress distribution in prosthetic ligaments that causes failure is very complex and not yet understood. Therefore, we have begun to develop a Finite Element Model of a prosthetic ACL. Here we describe the normal and contact stresses in Dacron(TM) yarn (a multi-fibrillar structure) using input data based on experimental measurements of the load and strain of six designed yarns. The results show that the normal and contact stresses in the fibres of the ACL yarn are directly proportional to the yarn strains. Increasing the twisting length (transverse deformation) of the yarn increases the normal stress in the fibres and the yarn modulus, but decreases the contact stresses between the fibres. The structural properties of a yarn are dependent on the specific arrangement of various filament types. Increasing the distance between the longitudinal (symmetry) axes of the filaments and the axis of symmetry of the yarn decreases the stresses.