The human motor system is organized for execution of various motor tasks in a different and flexible manner. The kinetic redundancy in the human musculoskeletal system is a significant property by which the central nervous system achieves many complementary goals. An equilibrium-based biomechanical model of isometric three-dimensional exertions of trunk muscles has been developed. Following the definition and role of the uncontrolled manifold, the kinetic redundancy concept is explored in mathematical terms. The null space of the kinetically redundant system when a certain joint moment and/or stiffness are needed is derived and discussed. The aforementioned concepts have been illustrated, using a three-dimensional three-degrees-of-freedom biomechanical model of the spine with 18 anatomically oriented Hill-type-model muscle fascicles. The considerations of stability and its consequence on the internal loading of the spine and coactivation consequences are discussed in both general and specific cases. The results can shed light on the interaction mechanisms in muscle activation patterns seen in various tasks and exertions and can provide a significant understanding for future research studies and clinical practices related to low-back disorders. Alteration of recruitment patterns in low-back-pain patients has been explained on the basis of this biomechanical analysis. The higher coactivation results in higher internal loading while providing higher joint stiffness that enhances spinal stability, which guards against spinal deformation in the presence of any perturbations.