This study developed a general methodology for probabilistic service life prediction of a composite viscoelastic cylindrical structure under random outdoor environment. The analysis emphasized both the statistical variations of environmental thermal loads and of material properties. The daily probability of failure was calculated considering failures due to both the excessive stress and strain. The probabilistic service life was then obtained via the evaluation of cumulative hazard function. Models for the deterministic and random variations of environmental thermal loads- ambient temperature, sky radiation, wind convection, and solar radiation, were developed and were considered in obtaining the structure's surface temperature. The statistical characteristics such as the mean and variance of the induced stresses and-strains were calculated via the uses of complex frequency response functions. Methods for statistical characterization of time and temperature dependent viscoelastic material properties were presented. Five statistical distributions- Normal, Log-Normal, Beta, Gamma, and Weibull, were considered for the goodness of fit. Two forms of material deterioration- time and temperature dependent aging and cumulative damage due to loading were also recognized. Three statistical distributions- Normal, Log-Normal, and Weibull, were used to represent the variations of induced daily maximum stress and strain. The daily probabilities of failure due to the maximum stress and strain were calculated based on the concept of load and resistance interference. The effects of these failure modes were then combined to define daily probability of failure of the structure. / Doctor of Philosophy