We study the flow behavior of a model soft glassy material - an aqueous suspension of Laponite - when it is squeezed between two circular parallel plates of different roughness. Aqueous suspension of Laponite shows a time dependent aging behavior as reflected in increased elastic modulus as well as yield stress, both of which however also decrease with an increase in the strength of deformation field thereby demonstrating typical thixotropic character. In a squeeze flow situation, under both force as well as velocity controlled modes: we find the behavior to be independent of the initial gap between the plates. In a constant force mode, the gap between the plates decreases until it reaches a finite limiting value, which is found to increase with an increase in age of the material as well as with a decrease in the applied force. In constant velocity experiments, at large gaps between the plates, normal force varies inversely with plate separation. The normal force is higher for a sample aged for a longer time as well as for a larger velocity of the top plate. We observe that the experimental behavior follows prediction of Herschel-Bulkley model solved for the squeeze flow (with different friction coefficients at the two plates) reasonably well under weak deformation fields. However, under strong deformation fields, experimental behavior deviates significantly from the prediction of Herschel-Bulkley model. This deviation arises due to melting or partial yielding of Laponite suspension under large deformation fields causing decrease in the viscosity, elastic modulus and the yield stress. (C) 2011 Elsevier B.V. All rights reserved.