A semianalytical method for calculating the time of fast relaxation in surfactant solutions with cylindrical micelles has recently been developed on the basis of the Becker-Doring kinetic equations. This method enables one to make the calculation procedure substantially shorter with no loss in the accuracy. A model micelle having the shape of a prolate ellipsoid was there used to determine the kinetic coefficients of monomer attachment to an aggregate because the problem of finding the diffusion flux of monomers to a micelle has an analytical solution for this model. In this work, the diffusion flux and fast relaxation time have been numerically calculated in terms of a more realistic model of a micelle having the shape of a spherocylinder. The results obtained have been compared with previously known ones.