A beam without attachment is called the unconstrained beam and that carrying attachment (s) is called the constrained beam. The object of this paper is to perform the free vibration analysis of a beam carrying multiple two-dof spring-mass systems by means of finite element method. From the presented numerical results, it is found that the mass, mass moment of inertia, spring constant and distances between center of gravity and two springs of the two-dof spring-mass system and its distribution on the beam have significant influence on the free vibration characteristics of the entire vibrating system.