Because of the flat slope of the magnetic characteristic curves at high saturation, the transformer inrush current peakes may assume an extreme magnitude. Even though such is rarely any danger to the transformer itself, the currents can cause serious problems in associated apparatus. This paper has analyzed various limiting factors of excess inrush currents, and then has suggested how to determine the frequency of encountering the inrush current peaks higher than an arbitrarily chosen value by deriving the probability equations of inrush current occurrence.