Connective soft tissues such as intervertebral disc, knee meniscus and articular cartilage are primarily made of water, proteoglycans, and collagen fibrils. The structural organization and relative content of these components as well as the type of collagen and proteoglycan, however, vary from tissue to tissue resulting in substantial differences in mechanical response under applied loads/deformations in different tissues and in different directions. The collagen fibres primarily influence the behavior of the tissue in tension relegating the compression carrying task to remaining components, the solid portion of which is referred to as the tissue matrix. In doing so, each component plays a mechanical role for which it is best suited. A homogeneous anisotopic simulation can adequately account for the observed direction dependent material properties of soft tissues. It cannot, however, represent the distinction between the matrix and collagen fibres in that while they may be both undergoing the same strain in the same direction, the stresses could be quite different and even in opposite directions. Such a response becomes evident when considering, for example, the lateral expansion of a tissue specimen in response to an axial compression load generating tension in fibres and compression in matrix so that these two internal forces cancel each other out resulting in no net lateral force. Proper consideration of this phenomenon requires the simulation of the tissue as a nonhomogeneous composite of a fibre reinforced medium. In this work, we will present the finite element studies of such arrangements and compare the predictions with those based on equivalent homogeneous direction-dependent material properties. The emphasis in the presented results will be placed on our studies on the disc anulus fibrosus.