Low-Level radioactive wastes generated in government and commercial operations involving nuclear materials need to be isolated from the environment almost in perpetuity (at least for 300 to 500 years or, in some cases, even longer). An increasing number of disposal sites are using concrete/metal barriers (so called “engineered” barriers) to isolate these wastes from the environment. Two major concerns hamper the use of engineered barriers; namely, the lack of ability to predict reliably the service life of these barriers and to estimate the confidence level of the service life predicted. Computer codes (SOURCE1 and SOURCE2) for estimating the long-term (centuries to millennia) service life of these barriers are presented. These codes use mathematical models (based on past observations, currently accepted data, and established theories) to predict behavior into the future. Processes modeled for concrete degradation include sulfate attack, calcium hydroxide leaching, and reinforcement corrosion. The loss of structural integrity due to cracking is also modeled. Mechanisms modeled for nuclide leaching include advection and diffusion. The coupled or linked effects of these models are addressed in the codes. Typical outputs from the codes are presented and analyzed. These results suggest that major efforts (including research) are needed to compare, evaluate, verify, and eventually validate codes (such as SOURCE1 and SOURCE2) for predicting the long-term behavior of engineered barriers.