The effect of a random transport cross section on the transverse spreading of a pencil beam of charged particles is analysed using the Fermi approximation to the 3D transport equation, in conjunction with a Gaussian model of cross section fluctuations. Stochasticity is seen to enhance the spreading of the beam but ensemble averaged quantities such as the transverse spatial moments and the scalar flux appear not to be sensitive to the details of the underlying statistical model. Furthermore, only asymptotic solutions for the scalar flux are possible because of divergent behaviour that can be traced to an inconsistency between the assumption of forward peakedness of the angular flux. which underlies the Fermi approximation, and the spreading induced by the randomness of the material properties.