Tough polymers (especially crystalline polyolefins) tend to show brittle behaviour, with a pronounced drop in fracture toughness, at high crack speeds. Since this effect is of special industrial importance, the High Speed Double Torsion test has been developed to measure it. Extracting fracture resistance data from the test demands accurate dynamical stress analysis of the specimen, but bulk strains are usually large enough to induce pronounced stress-strain non-linearity. The Torsional Impedance test was devised to acquire shear stress-strain data for corresponding geometries and loading times. The original analysis is here shown to have been flawed and it is corrected according to a more complete model, implemented as a numerical finite-difference scheme. Data are presented for modified high density polyethylene, and for pure and rubber-toughened grades of both polyoxymethylene and polypropylene.