The one—speed neutron transport equation with strong forward and backward scattering (characterized by α and β) has been solved analytically for an infinite slab with a finite order Snmethod. It is shown that the solution changes smoothly as c(α + β) passes unity. For a fixed criticality factor,c, a finite thickness is obtained both for α + β = 1/cand = 1. When the number of directions goes to infinity, the critical slab thickness vanishes at c(α + β) = 1. The total flux is then asymptotically given by a cosine function going to zero at the boundary. This is in contrast to the integral equation, which gives a different flux distribution. The results are supported by numerical calculations using the S4, S16and S96approximations.