The rheological characterization of a number of industrial and consumer fluids is considered. Experimental measurements of the fluid’s linear viscoelastic, non-linear viscoelastic and steady shear response are presented. A model originally developed for the description of polymer melts is then extended to test its applicability on an associative thickener, shampoo, a liquid crystalline polymer, tomato ketchup, an oil-based paint, and a kaolinite slurry. The oscillatory linear viscoelastic data are fitted to a discrete set of Maxwell elements and the non-linear step-strain data to a Wagner-type damping function. A factored time and strain dependent constitutive equation is then found in general to predict adequately the non-linear steady shear response. The rheological scheme has useful potential both for characterization and numerical prediction of engineering and processing flows.