In the sterilizing process of canned food in oil for a fish meat such as tunny, the slowest heating or cooling point is very important for the thermal process determination of the ran. To obtain the slowest point, the temperature profiles in solid food are estimated by numerical calculation from the fundamental equations at unsteady state in consideration of a free convection in the space occupied by the oil.The positions of the slowest heating or cooling point in the canned food in oil are obtained accurately, and a correlative equation for the position is obtained numerically under various operating conditions. The calculated temperature profiles and the position of both slowest points are in sufficiently good approximation to the experimental ones.