Piping flexibility analysis is done to ensure structural integrity in all operating conditions that may occur over the life of a system, whether static or dynamic. In industrial designs generally the rigidity of the support is neglected in the analysis of flexibility. The work presents an evaluation of the loads transmitted the structures in function of the rigidity of the pipe support. The evaluation was done through computer simulation using finite element techniques. The computational simulation made possible the evaluation of the forces transmitted to the support structures of an existing project of an orifice station, when considering the rigidity of the support. The work also shows that it is possible to refine projects when taken into consideration the influence of the rigidity of the supports, making a more adequate sizing the structure, portraying more faithfully the behavior of the system. The work also evaluates the influence, advantages and disadvantages in the use of stiffness in the supports with regard to the load transmitted to the support structures (support, base and tube).