Laplace's law constrains how thin the ventricular wall may be without experiencing excessive stress. The present study investigated constraints, imposed by myocardial viscosity (resistance to internal rearrangement), on how thick the wall may be. The ventricle was modeled as a contracting, spherical shell. The analysis demonstrated that viscosity generates stress and energy dissipation with inverse fourth- and eighth-power dependence, respectively, on distance from the cavity center. This result derives from the combination of squared dependence of viscous forces on shearing velocity gradients and the greater shear rearrangement required for inner layers of a contracting sphere. These predictions are based solely on geometry and fundamentals of viscosity and are independent of material properties, cytoskeletal structure, and internal structural forces. Calculated values of energy and force required to overcome viscosity were clearly large enough to affect the extent of thickening of the left ventricle. It is concluded that load-independent viscous resistance to contraction is an important factor in cardiac mechanics, especially of the thickened ventricles of concentric hypertrophy.