Currently, the flow of non-Newtonian fluids is present in many industrial processes and also in day-to-day of all. In this dissertation, initially it is exposed a new constitutive equation capable of modeling fluids that present as much elasticity as viscoplasticity, and this new model is called as Elasto-viscoplastic. For better understanding of this model, previously, a brief review of non- Newtonian fluids is done, with a focus on the SMD viscoplastic model and on the Oldroyd-B viscoelastic model, both which have a great influence in this new constitution model.Afterward, a new methodology of non- dimensionalization is presented, taking into account only the rheological parameters in this process and ensuring the independence of equations with respect to flow. Finally, the simulation of this new model is performed in a flow within a abrupt expansioncontraction geometry. In this simulation, it is studied the behavior of the fluid through this cavity with respect to key variables of the constitutive equation. The simulation was carried out by the finite element method and, by the analysis of the results, it is shown the influence of the rheological Deborah, flow speed, the power-law exponent and the ratio of the time of retardation and relaxation on the head loss and the flow pattern.