The dynamic response of a beam subjected to a moving mass is of a great importance among civil and mechanical engineers, due to the dynamic stresses induced in elastic structures. This classic problem has been studied since long ago and has been the subject of numerous investigations by applying different simplifications and methods. In this thesis, first the equation of motion of an Euler-Bernoulli beam subjected to a moving concentrated mass is obtained by both Newton-Euler and energy method. The equations are then extended to a moving elastic beam problem. For both cases, the results obtained from the homotopy analysis method are compared to those from a numerical code. Perturbation methods are efficient semi-analytical methods to solve weakly nonlinear equations and are capable of studying the stability of the response, bifurcation analysis, different resonances and other properties of nonlinear systems. In the next chapter, a perturbation method called multiple time scales is used to find the dynamic response of a nonlinear beam due to the large deflection and large deformation under the action of a moving mass. Many researchers have been of the opinion that the parameters which are usually neglected in a problem may have a significant influence on the results. There are numerous simplifications in the problem of a beam with moving mass each one could have a great effect in special situations on the response of the beam. For example, one can say about inertial effect containing Coriolis and centripetal forces, mass-sprung model and many others. One important parameter that can affect the result of the problem is the velocity. While in most of the studies, the assumption of the constant velocity has been utilized during the solution, there are few investigations in which the effect of the variable speed is taken into account. This variation in speed can occur as a result of the external or friction forces applied to the moving mass. Another chapter of the thesis is dedicated to investigating the effect of the traction, braking and friction forces applied to the moving mass on the dynamic response of a beam. Nonideal supports are one of the failures in structures. In addition to natural frequencies, the amplitude of the vibration is directly depended on the boundary conditions. Unlike idealized support conditions assumed in almost all of the investigations, there may be small deviation from this ideal condition in real systems. For example, for a hinged-hinged beam, because of the fact of the existence of small gaps or friction, there is a small displacement and moment at the supports which makes the equation of motion to an inhomogeneous one. The dynamic response of a simply supported beam with nonideal boundary conditions subjected to a moving mass is studied in another chapter. The solution procedure in this case and how the inhomogeneous problem was transformed into the homogeneous one is described. Finally, the dynamic behavior of a beam subjected to a moving mass with horizontally base excitation is studied and the results are reported in details. Keyword: euler-bernoulli beam, moving concentrated mass, moving elastic beam, homotopy analysis method, perturbation methods, braking force, nonideal boundary condition.