It is possible to alter the interaction parameters characterizing neutral particle radiation transport without significantly altering the spatial distribution of the particle fluence rate. Practical mathematical relations specifying the constraints that such an alteration must satisfy are known as similarity relations. Similarity relations are derived in this work from integrated versions of the single energy neutral particle transport equation. The application of these relations in accelerating Monte Carlo deep penetration simulations is described and assessed. Computational reductions may exceed a factor of 10 in highly scattering media in which the scattering is highly forward peaked, such as applies to the propagation of red and near IR light through soft tissues.