The determination of the parameters of viscoplastic fluids subject to wall slip is a special challenge and accurate results are generally obtained only when a number of viscometers are utilized concomitantly. Here the characterization of the parameters of the Herschel-Bulkley fluid and its non-linear wall slip behavior is formulated as an inverse problem which utilizes the data emanating from capillary and squeeze flow rheometers. A finite element method of the squeeze flow problem is employed in conjunction with the analytical solution of the capillary data collected following Mooney's procedure, which uses dies with differing surface to volume ratios. The uniqueness of the solution is recognized as a major problem which limits the accuracy of the solution, suggesting that the search methodology should be carefully selected.