Abstarct: One of the most important and applicable discussions in engineering sciences and in the area of the vibrations is the evaluation of structures under the vibrating loads. Including them is the rail industry. This is for a while that the analysis of vibrations resulting from the train on the rail road , has been noticed by experts and researchers .In this paper, review the out of plane vibration of a horizontally curved beam resting on a viscoelastic foundation and under a moving load. One of the necessities of doing this research is its application in the rail industry of the country. Generally, on the curve of the railway path, the track becomes as a model in the form of a horizontal curved beam (sometimes in a percentage of allowed cross and linear slopes) along with its substructure in the form of viscoelastic bed. For this purpose, first equations ruling over the system are gained and in the following free vibrations analysis is done using three methods of Galerkin method, numerical solution by Matlab software and solving in the finite element method with the help of COMSOL software and mentioned methods are validated and then forced vibrations under a moving load is analyzed which includes stability issue and critical speed. This method of analyzing is a new and applicable one from identifying the existing dilemmas aspect in designing the country’s rail system and removing current challenges on its way.