Recently, special considerations must be taken for accidents caused by corrosion, wear and ther·mal stress in main parts of the large marine diesel engine because of the temperature increase of combustion gas resulting from the supercharge by the exhaust gas turbine and the utilization of bunker oil. Piston crown is one of the parts which have heavy local temperature rise and thermal stress as the result of exposure to this high temperature combustion gas. According to stress calculations, maximum stress of piston crown is generated at first piston ring groove and, at the working condition of the engine, the fluctuating stress by gas pressure is superposed to statical thermal stress. If these superposed stress is larger enough than yield strength of the material employed, the high residual stress in reversed direction occurs by the stop of the en gine. In this way the stress is repeated in reversed directions over the yield strength of the material in the worst case. We discussed a method of calculation of stress mentioned above and some points to be specially considered for the strength of machine parts which show such a complicated stress hysteresis.