As time-variant reliability approaches become increasingly used for service life prediction of the aging infrastructure, the demand for computer solution methods continues to increase. Effcient computer techniques have become well established for the reliability analysis of structural systems. Thus far, however, this is largely limited to time-invariant reliability problems. Therefore, the requirements for time-variant reliability prediction of deteriorating structural systems under time-variant loads have remained incomplete. This study presents a computer program for $underline{REL}$iability of $underline{T}$ime-Variant $underline{SYS}$tems, RELTSYS. This program uses a combined technique of adaptive importance sampling, numerical integration, and fault tree analysis to compute time-variant reliabilities of individual components and systems. Time-invariant quantities are generated using Monte Carlo simulation, whereas time-variant quantities are evaluated using numerical integration. Load distribution and post-failure redistribution are considered using fault tree analysis. The strengths and limitations of RELTSYS are presented via a numerical example.