The purpose of this research is to study dynamic analysis of a beam using Modal Analysis. At the beginning, dynamic analysis of a beam subjected a single moving load or mass is investigated. Also, then beam dynamic behavior is studied under two moving loads or masses. Two loads or masses may have the same or different velocities. Different types of supports are considered for the beam analysis. Distribution of bending moments and shear forces along the beam are obtained. Finite element method is used to verify some of the results obtained by the analytical method. The beam is also studied for the failure situation (critical state) with different boundary conditions.