Abstract Insulation systems are critical components of the international thermonuclear experimental reactor (ITER). They must meet the super conducting magnets design requirements, including mechanical strength under combined shear and compressive stresses at cryogenic temperatures. Past cryogenic magnet systems often relied on woven glass/epoxy materials for insulation. An important point is to find a reliable shear/compression test method for these materials. The present work investigates a commonly used shear/compression setup and aims at measuring the reliability of the obtained test results. Therefore, the stress and failure analysis is performed analytically and numerically using the finite element method. The model is based on woven glass fiber reinforced materials which are subjected to combined shear and compressive stresses as well as to thermal loading, that results from cooling from 293 K to the test temperature of 77 K. A short analytical section shows the problems of common failure criteria which are used to describe the interaction of the shear and compression stresses. The numerical—finite element—section is based on three-dimensional linear elastic finite element models under thermo-mechanical loading. The locations of high stress gradients are investigated using an average stress criterion. Three different model geometries (15°, 45°, and 70°) are analyzed and finally compared with respect to their reliability.