We calculate the finite volume mass gap M (L) at 3-loop level in the non-linear O(n) σ-model in two dimensions in small volumes. By applying the Monte Carlo measurements of the running couplingḡ 2 (L) = 2nM (L)L/(n − 1) by Lüscher, Weisz and Wolff [1] measured in units of the physical mass gap m, the result is used to determine m in units of the Λ-parameter in the O(3) and O(4) models. Our determinations show good agreement with those by Hasenfratz, Maggiore and Niedermayer [2,3] in both models. We note that this manuscript has been revised in our paper hep-lat/9810025 by using the corrected four-loop β-function on the lattice.