Using the effective medium approximation the analytical decision of the calculation problem of the effective conductivity tensor of a polycrystalline medium with the uniaxial weakly depressed texture has been obtained. The polycrystalline medium is considered to consist of one-type spherical crystallites. To take into consideration the crystallites' orientations the rotation group representations theory has been used. The generalization of the decision for a case of triaxial textures has been obtained.