With the scenario of reliability estimation, a geometrically complex mechanical/structural component with multiple damage sites should be treated as a system, since there are many links (damage sites) of similar failure probabilities on any of such a component and the failures of the individual damage sites are not perfectly dependent of each other. Conventional system reliability model is not applicable to such a system because of the statistical dependence among the element (damage site) failures. To estimate the reliability of a mechanical system (or a complex component) in which element (damage site) failure dependence plays an important role, a model capable of reflecting the effect of element failure dependence is necessary. The present paper develops models which can deal with multiple damage sites and multiple failure mechanisms, reflect the dependence among element failure events and that among different failure modes. Such models are applicable to both typical mechanical systems and various components.