Beams might be subjected to impact loading which is a particular type of dynamic loading during their service lives. In this study the behaviour of beams under low speed impact loading has been investigated analytically. Simply supported and fixed ended beams have been analyzed with the assumption of rigid plastic behaviour. The collapse mechanism has been assumed to emerge by the instant formation of plastic hinges, hence, a limit analysis has been performed under dynamic loading considering the conservation principles of energy and momentum. The behaviour of rigid plastic beams under impact loading has been compared to the behaviour of elastic beams under similar loading conditions.