Cross sections for e-He(2 1 L) scattering have been calculated in the energy range 1 ≦ E ≦ 4 eV. For l > 0 partial cross sections a simple analytical method, proposed by the authors before, which is essentially an extension of Seaton's exact resonance method, has been applied. In the case l = 0, when a complex "angular momentum quantum number" in the rotated space appears, a matching procedure has been adopted, making use of a more realistic model potential. The results for Q(2 1 S-2 1 S), Q l (2 1 S-2 1 P) and Q(2 1 P-2 1 P) cross sections are compared with other theoretical calculations and in the case of the elastic Q(2 1 S-2 1 S) cross section with the available experimental data as well. The applicability of the analytical method used in the electron-atom scattering calculations is discussed, in particular for those processes which play a dominant role in the Stark broadening of spectral lines from plasmas. Finally, the relevance of the present method to searching for an eventual resonant (or virtual) state near 2 1 S threshold has been discussed.