This study reports on the preparation of linear models of grinding, grinding-classification, classification-grinding, and classification-grinding-classification circuits based on material balances supported by population balances. For these procedures, particles were described by size and chemical composition, and the parameter phi is introduced which represents the fraction of one class of particles which delivers material to another. An index is introduced to evaluate the effect of the proposed circuits on the characteristics of the floatability of the material. The methodology can be amplified to include other types of circuits, and the models can be used to evaluate, compare, and select grinding circuits with classification. As examples of their application, some of these models are used for the synthesis of flotation circuits, following the methodology employed by [Cisternas, L., Mendez, D., Galvez, E., & Jorquera, R. (2006). A MILP model for design of flotation circuits with bank/column and regrind/no regrind selection. International Journal of Mineral Processing, 79(4), 253-263] with some variations, showing how the selection of these circuits can affect the design and yields of a mineral processing plant. (C) 2008 Elsevier Ltd. All rights reserved.