An optimal control is giyen for regulating power distribution in a nuclear power reactor which has cylindrical geometry. The space dependence of the system is described by expanding space depenident variables by Helmholtz modes. Results are obtained through the principle of optimality and are described by the Riccati-type algebraic equation that the optimal feedback coefficients should satisfy. Use of an integral equation as the system equation makes it possible to deal with actual controlling apparatuses: control rods or rod clusters.