In order to examine the compression-shear combined mechanical properties of rubber fiber concrete, an experimental study was carried out on rubber fiber concrete of three different configurations using a material compression-shear testing machine by considering different axial compression ratios. The failure modes and shear stress-strain curves of rubber fiber concrete under different loading conditions were obtained. By comparatively analyzing the mechanical parameters of rubber fiber concrete under different axial compression ratios, the following conclusions were drawn. With the increase of the axial compression ratio, the failure mode in the shear direction gradually developed from a relatively straight crack to a main crack accompanied by a certain amount of axial cracks; meanwhile, the number of concrete slags on the shear failure section was gradually increased and the friction marks were gradually deepened. The addition of rubber particles increased the randomness and discreteness of the concrete upon failure, while fibers inhibited the development of oblique micro-cracks and the dropping of concrete slags. The shear stress of the concrete specimen containing rubber particles was significantly lower than those without rubber particles. Comparatively, fibers showed little effect on the shear stress. As the axial compression ratio increased, the shear stress and shear strain of rubber fiber concrete were gradually increased, but the increasing amplitude of shear stress tended to become flattened. Under the influence of the axial compression ratio, the shear stress of C-0%-0%, C-30%-0%, and C-30%-0.6% was increased by 4.57 times, 3.26 times, and 2.69 times, respectively, suggesting a gradually decreasing trend. At the same time, based on the principal stress space and the octahedral stress space, the compression-shear combined failure criterion was proposed for the three different rubber fiber concretes. The research findings are of great significance to the engineering application and development of rubber fiber concrete.