The recently developed H-N method is used to solve the critical slab problem for a slab which is surrounded by a reflector. In the special case: for R = 0 (the reflection coefficient) the problem reduces to the one under vacuum boundary conditions. It is shown that the method is concise and leads to fast converging numerical results. The presented numerical results are compared with the data available in literature. (C) 2004 Elsevier Ltd. All rights reserved.