A technique is illustrated for finding an estimate of the Stirling numbers of the second kind, Sn, r(1 ⩽ r ⩽ n), as n → ∞, for a certain range of values of r. It is shown how the estimation can be found to any given degree of approximation. Finally, the location of the maximum of Sn, r (1 ⩽ r ⩽ n) and the value of the maximum are computed.