Our research focused on the deformation behavior of a strongly textured magnesium alloy (formed by Equal-Channel Angular Pressing: ECAP) under compression shear loading. For compression shear loading a special sample geometry is used: the specimen has a cylindrical shape, but the top and bottom surfaces are cut at an angle with an inclination of about 6°. This leads to a preferred shearing-direction within the sample (short vs. long diagonal) during nominally uniaxial compressive loading. This unique mechanical test, due to its special specimen design, and in combination with anisotropic properties in the textured samples, leads to special crack propagation and fracture behavior of the material. The severe deformation process ECAP leads to a distinct, strong texture in the magnesium alloy, where the basal planes are oriented parallel to the ECAP shear plane. After this severe plastic deformation process, compression shear specimens were taken out of the material oriented in two directions with respect to the last shear plane induced by ECAP (parallel and anti-parallel). The specimens were deformed in compression shear at three different strain rates (0.001, 1, 100 s-1; all tests were performed at room temperature). A digital image correlation (DIC) system was used to document the surface strain fields in-situ during all experiments. Our tests revealed that texture dominates material behavior even under very specific test conditions: at lower strain rates, deformation and fracture does not occur along the expected (due to the specimen design) shearing direction, but is instead determined by the orientation of the ECAP shear plane even when maximum shear stresses would favor another fracture plane. At high strain rates the material fails in the direction of the highest shear stress, which is most likely related to a more pronounced effect of adiabatic processes. We discuss these experimental findings in the light of complementary results of elastic Finite Element simulations, to obtain a broader view on how stress propagation is related to the geometry of the compression shear sample.