For polydisperse suspensions with equal-density solid particles and continuous particle size distribution, design and operation methodologies of a liquid fluidized bed classifier (LFBC) are introduced, both based on a modified version of the generalized clarifier-thickener (GCT) model presented by Bürger, García, Karlsen, y Towers (2008) Computers and Chemical Engineering 32, 1181-1202. The LFBC is a special case of the GCT characterized by an upwards-directed flow of liquid at the lower end of the unit. Moreover, a versatile way to discretize the particle size variable for the numerical solution of this equation is presented. Numerical examples illustrate the performance of the model and the effectiveness of design and operation methodologies.