In this investigation, the problem of the response of beams subjected to a moving mass has been studied. The main objective in this thesis is to provide easy and acceptable solutions for this problem. Three different methods of solution are presented. (I) The first method demonstrates the transformation of a familiar governing differential equation into a new solvable series of ordinary differential equations. (II) The second method discusses the solution of the same problem based on a new discrete element model for beams. (III) The third method is based on a finite element technique. The computer program used in this investigation is called PAFEC. The validity of the solutions is ascertained by comparison. Furthermore, the study shows that the response of beams due to a moving mass, which has often been neglected in the past, must be properly taken into account because it often differs significantly from the moving load model. Based on the cost of computations and desirable accuracy, a designer can choose the appropriate method.