A new computational model for neutral particle transport in the outer regions of a diverted tokamak plasma chamber is presented. The model is based on the calculation of transmission and escape probabilities using first-flight integral transport theory and the balancing of fluxes across the surfaces bounding the various regions. Both long and short mean free path regions can be handled. The complex geometry of the outer regions of a diverted tokamak can be represented accurately and economically using precomputed probabilities which depend only on the mean free path of the region. Benchmark comparisons with Monte Carlo illustrate that quite accurate results may be expected with the method