The extrapolation distance in the cylindrical Milne problem (“black” cylinder immersed in a homogeneous, infinite, isotropically scattering and absorbing medium) is calculated in one- and two-group approximations. The method used consists of asymptotic expansions in 1/R and R (R being the radius of the cylinder) for large and small R, respectively, and of a variational method for R = O(1), R measured in mean-free-paths. The numerical results are given for two cases in the one-group (c = 0.90 and c = 0.95) and for two cases in the two-group approximation (both for κ = 1). The results show convergence of the methods and sufficient accuracy of the applied numerical procedures. This conclusion is confirmed by the comparison of the values of the extrapolation distance calculated by variational and asymptotic expansion formulas in regions of R, where both can be applied.