A simplified formula for radiation streaming through bent ducts was previously derived by optics analogy, considering only components passing through the duct and without enormous preparatory calculations. Now, by taking account of deep penetrating component, the streaming formula is improved in order to estimate not only γ -ray flux but also neutron flux with accuracy, factor 2-3, applicable to preliminary shielding designs. Dose rates at the exit estimated by the improved formula are compared with experimental values. As for γ -ray evaluated values become conservative by improvement, while evaluated values were underestimated before improvement. Also for neutron, the discrepancy between the calculated values by the present formula and observed ones becomes within factor 2 after improvement from factor 3 before improvement. From these results, it is concluded that the improved formula is applicable to preliminary shielding designs.