The left ventricle (LV) is modelled as a fluid-filled, thick-walled finite-elasticity cylindrical shell, subject to internal pressure increase during isovolumic contraction. Our objective is to elucidate that the tremendous internal pressure build-up during isovolumic contraction is caused by stress development in the spirally-wound myocardial fibers due to their contraction. The LV model data consists of LV chamber pressure, LV dynamic geometry and LV twist angle. In our analysis, the LV chamber pressure increase and LV (radial, longitudinal, and twist) deformations are formatted to be caused by the contractile stresses in the LV myocardial fibers (based on the hyper-elastic constitutive property of the LV myocardial wall, expressed in terms of the strain energy density function). The LV wall stresses are expressed in terms of the strain energy density function, and hence in terms of the measured LV wall strains and the material parameters. Then, by satisfying the stress boundary conditions, from the measured data on LV deformation state and LV pressure, we first determine the LV wall's constitutive properties, and then the instantaneous stress state in the LV. The stress generated in the LV cylindrical model is equivalent to the development of active compression force and torsion within the model, as a mechanism for the high intra-LV cavity pressure build-up during isovolumic contraction. We in turn adopt (i) the principal compressive stress to be the stresses developed in the myocardial fibers (by their contraction), and (ii) the principal stress trajectory to correspond to the orientation of the myocardial fibers. The results show that the myocardial fiber orientation changes during the isovolumic phase, as the LV contracts. Hence, an important determinant of our analysis is the orientation of the myocardial fibers. Conversely, it can be said that the fibers are so optimally oriented, that their contraction causes LV deformation to in turn cause the appropriate increase in intra-LV pressure. Another important outcome of our analysis is the determination of the "LV torque vs twist angle" relationship, which has the potential to be employed as an index of contractility.