The Milne problem is generalized to include a specular and diffuse reflecting boundary. Linearly anisotropic case is studied using singular eigenfunction method. Multiplying and nonmultiplying medium are included in addition to nonabsorbing medium in the treatment. Accurate numerical results are generated by the first order approximation. These results are presented according to the variation of different parameters such as anisotropy, reflection coefficients and secondary neutrons per collision. (C) 2002 Elsevier Science Ltd. All rights reserved.