This work presents a methodology for the solution of the Navier-Stokes equations for Bingham and Herschel-Bulkley viscoplastic fluids using stabilized mixed velocity/pressure finite elements. The theoretical formulation is developed and implemented in a computer code.; Viscoplastic fluids are characterized by a minimum shear stress called yield stress. Above this yield stress, the fluid is able to flow. Below this yield stress, the fluid behaves as a quasi-rigid body, with zero strain-rate.; First, the Navier-Stokes equations for incompressible fluid are presented. A review of the viscoplastic rheological models is included, with a detailed description of these models. The regularized viscoplastic models due to Papanastasiou are described. Double viscosity regularized models are proposed as an alternative to the models commonly used.; The discrete model is developed, and the Algebraic SubGrid Scale (ASGS) stabilization method, the Orthogonal Subgrid Scale (OSS) method and the split orthogonal subscales method are introduced.; The methodology proposed in this work provides a computational tool to study confined viscoplastic flows, common in industry.

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