Critical literature review in this study revealed that there can be a significant influence of the residual stress on the engineering properties of rock. The review also showed that few number of research works on the quantification of the influence was attributed to the limitation of the two classical measurement techniques, viz, X-ray diffraction and mechanical relaxation method. In this study, a new way of approach was sought based on the assumption that residual stress up to the failure. A series of hoop tests conducted onthe samples from the limb of Carboniferous Limestone in Clevedon, England, revealed that (i) there is no preferential orientations of microcracks and minerals which have been widely believed as the main source of the strength anisotropy of rock; (ii) the anisotropy of the tensile strength of the limestone results from the influence of the residual stress; (iii) since jointing commenced within the fold, residual stored strain energy has been released preferentially in the direction perpendicular to the major joints(o$^{circ}$ and 90$^{circ}$); (ⅳ) during the hoop test making it much easier to create tensile fracture in these directons, viz 45$^{circ}$ and 135$^{circ}$)was released during the hoop test making it much easier to create tensile fracture in these directions, viz 45$^{circ}$and 135$^{circ}$;(v) the direction in which the stored strain energy may be presumed to be the least, required the greatest work to cause failure.