The paper studies the global methods in monitoring structural health. The principle of global methods is based on the structural dynamic theorems. There are four theories available; namely, (1) the random decrement theory, (2) the modal frequency theory, (3) the transmissibility theory, and (4) the modal shape theory. This paper addresses specifically the modal frequency theory and the transmissibility theory, and their application to the location of fracture damages and the intensity of the damages. The reliability and health assessment depends on the accurate modeling of the damaged structure. With the damage assessment, the paper proposes a method to estimate the upper bound of reliability of the structure, during the hysteretic cycling of the loading.