Thermal energy storage (TES) is an important practice implemented in a wide variety of renewable energy technologies. TES provides an effective means of thermal management and dispatchable energy. A novel idea of using isochoric containment of elemental sulfur as the energy storage media has been proposed. An important design criterion of this idea is the structural integrity of the storage container. Using both empirically developed analytical models from published studies and computational models, this paper analyzes the impact of internal pressure, temperature gradients, and the operating temperature on three different materials (SS 316, SS 304, Inconel 625) in a parametric study. The damage mechanisms that are studied are creep, low cycle thermomechanical fatigue, and thermal shocks. It is found that regardless of vertical or horizontal configuration, SS 316 and Inconel 625 survive the desired 20-40 year life for all pipe sizes at the fastest charging rate in the parametric study. Due to its susceptibility to creep deformation, thin schedule 5 pipe sizes of SS 304 fail before the expected 20 year life. The conclusion of this study is to employ SS 316 or Inconel 625 pipes for isochoric containment of sulfur in TES applications.