Structural failure is rarely a ''sudden death'' type of event, such sudden failures may occur only under abnormal loadings like bomb or gas explosions and very strong earthquakes. In most cases, structures fail due to damage accumulated under normal loadings such as wind loads, dead and live loads. The consequence of cumulative damage will affect the reliability of surviving components and finally causes collapse of the system. The cumulative damage effects on system reliability under time-invariant loadings are of practical interest in structural design and therefore will be investigated in this study. The scope of this study is, however, restricted to the consideration of damage accumulation as the increase in the number of failed components due to the violation of their strength limits.