This research is concerned with the application of extreme value theory to motor insurance generally, and, in particular, to motor insurance in the Egyptian market. Since this theory was introduced there have been many attempts to use it in some insurance fields, but very few attempts have been made to apply it to motor insurance and this attempt is the first to be made in the Egyptian market. In this particular attempt the aim is to study the likely benefit of the application of the theory within Egyptian experience; to attract the attention of underwriters to the shape of the claim amount distribution, especially at its extreme end so that they may be in a better position to protect their companies against unexpectedly severe claims. The research includes formulae representing the 10 1argest claims and an estimation of the 10 1argest claims which are expected to occur in the Egyptian market during the period 1977 to 1981 inclusive. The detailed and complete calculations are presented.