Several recent experiments have suggested that the structural-elastic properties of the native and the transition states of biomolecules are a key determinant of their mechanical stability. However, most of the current theoretical models were derived based on conformation diffusion of the molecule along a phenomenological energy surface, lacking a direct relation to the structural-elastic parameters of the molecules. Here, based on the Arrhenius law and taking into consideration of the structural-elastic properties of the native state and the transition state, we derived a simple analytical expression for the force-dependent lifetime of the native state of the molecules. We show that this model is able to fit a wide scope of experiments, and explain a variety of complex force-dependent transition kinetics observed in recent experiments. The results highlight a previously largely unrecognized structural-elastic determinant of the lifetime of biomolecules under force, and provide a new theoretical framework that can inform us the structural-elastic properties of the molecules.