Compressive or tensile loading of rocks results in anisotropic damage represented by microcracks. Disk specimens of a brittle limestone are initially loaded diametrically, introducing damage as recorded by acoustic emission measurements. Upon unloading, prismatic specimens are cut from the disks in different directions and are tested in uniaxial compression while measuring simultaneously the acoustic emission. An attempt is made to reveal the damage formed under triaxial loading with one of the principal stresses being tensile, by using the Kaiser effect in compressive uniaxial reloading. The results are of importance for the Kaiser effect applications for stress measurements in rocks where one of the principal stresses is tensile.