This paper deals with the problem of the instability regions of a free-free uniform Bernoulli beam consisting of two concentrated masses at the two free ends under the follower and transversal forces as a model for a space structure. The follower force is the model for the propulsion force and the transversal force is the controller force. The main aim of this study is to analyze the effects of the concentrated masses on the beam instability. It is determined that the transverse and rotary inertia of the concentrated masses cause a change in the critical follower force. This paper also offers an approximation method as a design tool to find the optimal masses at the two tips using an artificial neural network (ANN) and genetic algorithm (GA). The results show that an increase in the follower and transversal forces leads to an increase of the vibrational motion of the beam which is not desirable for any control system and hence it must be removed by proper approaches. Manuscript profile