One of the first applications of integral equation inversion techniques in rheology was the exact result of Weissenberg, which enables the shear curve to be obtained from a laminar pipeflow experiment. It is shown that numerical solution of the integral equations occurring for this and other common experiments may be used instead. Numerical inversion programs have been written for the pipeflow and Couette problems. Certain, more difficult inversions, arising with elastic fluid constitutive relations, are also treated; in some cases a simple version of the KBKZ theory seems fairly realistic over a wide range of experiments.