The objective of this work is to model computationally Bingham and Herschel-Bulkley viscoplastic fluids using stabilized mixed velocity/pressure finite elements. Numerical solutions for these viscoplastic flows are presented and assessed. The regularized viscoplastic models due to Papanastasiou is used. In the discrete model, the Orthogonal Subgrid scale (OSS) method is used. In this part II , numerical solutions for two problems of Bingham and Herschel-Bulkley confined flows are presented. The solutions obtained validate the methodology proposed in part I of this work.