The elastic and inelastic mechanical behavior of rubberlike and soft biological materials subjected to large deformation will be studies analytically and experimentally. The role of the molecular structure and effects due to prestress, preconditioning, and internal viscous damping will be investigated in technical and biomechanical applications. Equations that include the molecular chain number and predict the effect of preconditioning observed in tests on elastomers and soft tissues will be derived. The theory will be confirmed by experiments and applied to study the effect of preconditioning of arterial balloons used in various surgical procedures will be studied theoretically and in laboratory experiments.