An impact energy absorbing structure for attachment to the boss of a steering wheel in an automobile is disclosed. It comprises an energy absorbing member made of brittle plastic material and a cover member. It has empty spaces formed between the central part and the outer peripheral part of the energy absorbing member to give rise to an external wall part breakable under an impactive load in the outer peripheral part of the energy absorption member. Owing to this arrangement, the impactive energy absorbing structure of this invention is enabled to maximize the amount of energy absorption and enhance the energy absorption efficiency to a great extent.