Due to a high specific strength, magnesium alloys have a high potential to be considered for lightweight solutions in automotive industry. For the numerical design of forming processes, it is important to describe the yielding as well as the fracture behaviour of a material as precisely as possible. In order to fully characterise the fracture behaviour of an AZ31 magnesium sheet alloy at elevated temperatures, a heated test setup for uniaxial tensile machines was developed. The setup allows an adjustment of the load application angle whereby a stress variation is achieved in the centre of the specimen. In order to determine the fracture strain for different temperatures and for varying stress states, a shear stress specimen (also known as butterfly specimen) was considered to perform mechanical experiments by means of this setup. Using numerical simulations, the specific stress development and strain value in the fracture zone, which is needed to calibrate stress state fracture models, was determined for each loading angle and temperature. For this purpose, an orthotropic yield criterion CPB06, which is suitable for depiction of the particular flow behaviour of magnesium alloys (e. g. compression-tension asymmetry), was used. By this means, sufficient data for the calibration of common stress state based fracture models could be provided and the MMC- (Modified Mohr-Coulomb) fracture model was parameterised.