Many fluids used in industries have elastic characteristics and the study of these properties becomes important for processes such as emulsions stability and extrusion. In various industrial process operations involving polymeric materials, the extensional behavior has a very important role in the flow of fluids. Therefore a complete rheological characterization and development of constitutive models is essential in order to describe the behavior of the fluid considering the elasticity. The Boger fluid shows a Newtonian Behavior in shear flows and at the same time it’s highly elastic, so it becomes important in study of the processes mentioned above. This project consisted in a complete rheological characterization of a Boger fluid (PIB / PB) for different concentrations of short Wollastonite fibers (Calcium Silicate), aiming to analyze the effect of the addition of these fibers in viscoelastic fluid(Boger) behavior, and also the behavior of fibers orientation in flows which the elastic effect is important. A comparison between the Boger fluid and a similar viscosity Newtonian fluid(PB-Q) behaviors was also done in order to assess the effect of elasticity in a flow.