Adequate knowledge of the transmission probabilities of neutrons through control blades filled with round tubes containing absorbing material is required in reactor design. Starting from a strict formulation of the problem, some computational approximations are introduced which lead to compact expressions directly available to the designer. The accuracy of the proposed formulas is then investigated in conjunction with a theoretical and numerical analysis of the confidence limit of the most advanced method (P1 blackness theory) of accounting for control blades in diffusion calculations. Finally, comparisons with experimental integral data (Rossi-α measurements) confirm that the accuracy of the proposed formulas is consistent with the precision of the method.