Residual stresses in a stainless steel vessel containing glass have been evaluated using measurements and numerical simulation. High-level nuclear wastes are often vitrified in glass cast in cylindrical stainless steel containers. Knowledge of the internal stresses generated in both the glass and container during this process is critical to structural integrity and public safety. In this research, residual stresses were measured near the surface of a High Level Waste container using an Incremental Center Hole Drilling technique. Residual stress magnitudes were found to be at or near to the yield stress in the container wall. A transient finite-element thermal-stress model has been developed to simulate temperature, distortion, and stress during casting and cooling in a simple slice domain of both the glass and the container. Contact thermal-stress elements were employed to prevent penetration at the glass–container interface. Roughness of these contact surfaces was modeled as an equivalent air gap with temperature-dependent conductivity in the thermal model. The stress model features elastic-viscoplastic constitutive equations developed based on the temperature-dependent viscosity of the glass and elastic-plastic constitutive equations for the stainless steel. The simulation was performed using the commercial ABAQUS program with a user material subroutine. The model predictions are consistent with the residual stress measurements, and the complete thermal–mechanical behavior of the system is evaluated.