<p>Genesis and prediction of strength anisotropy in structured rock remain fundamental challenges in rock mechanics. This study proposes a structure tensor that quantitatively characterizes the scale and strength differences between rock and structural media, applicable to rocks or rock masses containing a single structure plane or layered structures. By projecting the stress tensor onto the structure tensor orientation, an anisotropic strength function is derived that physically represents the anisotropic weakening of hydrostatic pressure in anisotropic rocks, thereby capturing their strength anisotropy. This weakening effect results from the coupled effects of structure plane properties, their orientation relative to the stress state, and the magnitude of principal stress. Based on the functional dependence of strength on hydrostatic pressure, a general framework is proposed for extending isotropic strength criteria to anisotropic conditions by substituting the proposed anisotropic strength function in place of the isotropic rock strength term. To illustrate the framework, an isotropic criterion is selected and extended accordingly. Validation against triaxial test data from six typical anisotropy rocks confirms that the extended criterion precisely predicts both the U-shaped distribution of strength with respect to the angle <i>β</i>, defined as the angle between <i>σ</i>₁ and the dip direction of the structural plane, and the strength-strengthening effect governed by the angle <i>ω</i> between <i>σ</i>₃ and the structural plane dip direction. The resulting three-dimensional yield surface exhibits an asymmetric pyramid. This work clarifies the genesis of rock strength anisotropy and establishes a theoretical basis for transitioning between isotropic and anisotropic strength criteria.</p>