An obstacle in modeling aseptic processing of particulate foods is the lack of a reliable estimator for the drag force of the non-Newtonian liquid phase on the suspended particles as they flow through the holding tubes of such systems. The objective was to develop an expression for the drag force on cubic assemblies of spherical particles suspended in a pseudoplastic fluid flowing in a tube. An apparatus was assembled for direct measurement of the drag force exerted by solutions of sodium carboxymethyl cellulose (CMC) on the assemblies inside a tube. An empirical drag correction factor, as a function of particle volume fraction (applicable to Stokes’ law), was developed.