Thermal mechanical stresses of glass-ceramic to stainless steel (GCtSS) seals are analyzed using finite element modeling over a temperature cycle from a set temperature (T-set) 500 degrees C to -55 degrees C, and then back to 600 degrees C. Two glass-ceramics having an identical coefficient of thermal expansion (CTE) at similar to 16 ppm/degrees C but very different linearity of thermal strains, designated as near-linear NL16 and step-like SL16, were formed from the same parent glass using different crystallization processes. Stress modeling reveals much higher plastic strain in the stainless steel using SL16 glass-ceramic when the GCtSS seal cools from T-set. Upon heating tensile stresses start to develop at the GC-SS interface before the temperature reaches T-set. On the other hand, the much lower plastic deformation in stainless steel accumulated during cooling using NL16 glass-ceramic allows for radially compressive stress at the GC-SS interface to remain present when the seal is heated back to T-set. The qualitative stress comparison suggests that with a better match of thermal strain rate to that of stainless steel, the NL16 glass-ceramic not only improves the hermeticity of the GCtSS seals, but would also improve the reliability of the seals exposed to high-temperature and/or high-pressure abnormal environments.