This study examines thermal safety on three-way catalyst that dominates 70 % among whole exhaust gas purification device in 2003. Three-way catalyst durability in the Korea requires 5 years/80,000 km in 1988 but require 10 years/120,000 km after 2002. Three-way catalyst durability in the USA requires 7 years/120,000 km but require 10 years/160,000 km after 2004. Three-way catalyst maintains high temperature in interior domain but maintains low temperature on outside surface. Therefore this device shows tensile stress on outside surface. Temperature distribution of three-way catalyst was acquired by thermal flow analysis for predicted thermal flow parameter. Thermal stress analysis for three-way catalysis was performed based on this temperature distribution. Thermal safety of three-way catalyst was estimated by power law dynamic fatigue life estimation and strength reduction methods for thermal stress.