Mechanical properties of muscle tissue are crucial in biomechanical modeling of the human body. Muscle tissue is a combination of Muscle Fibers (MFs) and connective tissue including collagen and elastin fibers. There are a lot of passive muscle models in the literature but most of them do not consider any distinction between Collagen Fibers (CFs) and MFs, or at least do not consider the mechanical effects of the CFs on the Three-Dimensional (3-D) behavior of tissue. As a consequence, unfortunately, they cannot describe the observed stress-stretch behavior in tissue in which the reinforced direction is not parallel to the MF direction. In this research, a new passive muscle model is presented, in which the CFs are separately considered in the formulation: they are distributed along the MFs in a cross-shaped arrangement. Thanks to this new architecture, a mechanical reinforced direction can be proposed, in addition to the muscle main fiber direction.The passive biomechanical properties of the genioglossus muscle of a bovine tongue have been measured under uniaxial tensile tests. To characterize the 3-D response of the tissue, tests have been performed in different directions with respect to the MF direction. Moreover, a Constitutive Law (CL) has been proposed for modeling this behavior. In addition to our measurements on the bovine genioglossus muscle, results published in the literature on experimental data from the longissimus dorsi of pigs and the chicken pectoralis muscle were used to appraise the applicability of the proposed model. It is demonstrated that the proposed passive muscle model provides an accurate description of the fiber-oriented nature of muscle tissue. Also, it has been shown that using Finite Element Analysis (FEA) it might be possible to predict the angle θ between CFs and MF.