The Milne problem is investigated subject to reflecting boundary conditions. The original version of the problem with vacuum boundary condition is generalized assigning, to the surface x = 0, a reflection coefficient R(0 less than or equal to R less than or equal to 1). Linearly anisotropic case is studied using singular eigenfunction method. The cases of non-multiplying and multiplying medium are covered. The separate treatment of non-absorbing medium is also included. The singular eigenfunction method yields good accuracy with an optimized first order approach. Solution of the Milne problem is formulated in terms of characteristic parameters such as extrapolated endpoint, emergent angular distribution and total and asymptotic neutron densities. Numerical results for the analytically evaluated parameters are then presented. (C) 2000 Elsevier Science Ltd. All rights reserved.