This paper is concerned with the description of inherent anisotropy in porous media. First, a mathematical formulation is outlined for the specification of conditions at failure. The framework incorporates a scalar anisotropy parameter, which is defined in terms of mixed invariants of stress and microstructure-orientation tensors. The general approach is illustrated by several specific applications. These include description of the mechanical behaviour of sedimentary rocks, as well as formulation of a macroscopic failure criterion for structural masonry. The paper is concluded by a discussion on fabric descriptors and their identification using micro-CT measurements.