This article presents the theoretical basis for the yield plastic rheological model for shear-thinning mineral suspensions. The standard structural model is modified to allow for the hypothesis that the average interparticle bond strength increases as the structure (aggregates) breaks down. The resulting model is algebraically simple and contains the Newtonian, Bingham, and Casson models as special cases. If minor stresses are considered, the model will also describe suspensions with a low shear rate viscosity plateau (i.e., Carreau-type suspensions). The yield plastic model accurately describes the flow behavior of most shear-thinning suspensions and is consistent with the observed behavior in rheometers and pipelines.