The theoretical model of conductivity of a layered anisotropic normal metal containing small superconducting ellipsoidal granules with an arbitrary ratio of semiaxes is developed. Calculation data obtained under two simple approximations (self-consistent and Maxwell) are compared. The results may be applied in the analysis of the observed temperature dependence of the conductivity anisotropy in various anisotropic superconductors with the superconducting phase emerging in the form of isolated superconducting granules. The temperature dependence of the electric resistance along and across the conducting layers above and near the superconducting transition temperature is studied experimentally for bridge structures of a varying thickness. It is demonstrated that this resistance and even the effective superconducting transition temperature depend strongly on the bridge thickness (i.e., the number of layers through which the electric current flows). Note that significant differences were observed only for the resistance across the layers.