Foliated metamorphic rocks and laminated, stratified or bedded sedimentary rocks have properties (physical, dynamic, thermal, mechanical, hydraulic) that vary with direction and are said to be anisotropic. Rock mass anisotropy can be found in volcanic formations and sedimentary formations consisting of alternating layers or beds of different rock types. Rock masses cut by one or several regularly spaced joint sets are anisotropic in addition to being discontinuous. This paper deals with the subjects of rock anisotropy and rock stress. Both topics are important in rock engineering and are interrelated Rock fabric controls the build-up in in situ stresses in the Earth's crust, their magnitude and orientation. On the other hand, stresses and in particular compressive stresses tend to close microcracks or discontinuities thus making rock behavior non-linear and rock anisotropy pressure dependent. This paper is divided into three parts. In the first part, existing models to describe the deformability properties of anisotropic rocks as well as the laboratory and field methods to determine those properties are reviewed. Then, it is shown how to account for both rock anisotropy (intact and joint induced) and the curvature of the Earth when estimating in situ stresses in rock masses. Finally, the effect of anisotropy on the analysis of overcoring measurements with cells similar to the CSIR Triaxial Strain Cell is discussed.