The problem of converting capillary viscometry data with wall slip into a shear stress versus shear rate relationship and a wall shear stress versus slip velocity relationship is formulated as an integral equation of the first kind. This reveals the ill-posed nature of the problem. A procedure based on Tikhonov regularization is applied to find an approximate solution to this equation. This way of processing capillary viscometry data has the advantage that it does not require the assumption of a theological model to relate the shear rate and the slip velocity to the local shear stress. Since Tikhonov regularization allows for the ill-posed nature of the problem, it can be expected to give reliable results in the presence of experimental noise. The performance of this method is demonstrated by applying it to the capillary data for a linear low-density polyethylene, a high-density polyethylene, a suspension of ammonium sulfate particles in a viscous Newtonian carrying fluid, and a mineral-based aqueous paper coating color. In each case, Tikhonov regularization has succeeded in obtaining the maximum amount of information regarding the theological properties of the material and these properties are in good or reasonable agreement with published data. (C) 2003 The Society of Rheology.