Further development of the multiple collision method is presented. The critical condition for a monoenergetic neutron source was obtained by flnding the pole of a Laplace transform for total neutron variation with time. The socalled c, the mean number of secondaries per collision, was calculated within an error less than 10/sup -5/ for every critical system with finite thickness. The asymptotic total number of neutrons in the system after a sufficiently long time was also derived. Finally, comparing the derived critical condition with that from diffusion theory, the extrapolation distance was evaluated accurately for a system with thickness less than several times the neutron mean free path. (auth)