In this work we present a predictive analytical model that encompasses the performance and scaling characteristics of a non-deterministic particle transport application, MCNP. Previous studies on the scalability of parallel Monte Carlo eigenvalue calculations have been rather general in nature. It can be used for the simulation of neutron, photon, electron, or coupled transport, and has found uses in many problem areas. The performance model is validated against measurements on an AlphaServer ES40 system showing high accuracy across many processor / problem combinations. It is parametric with both application characteristics (e.g. problem size), and system characteristics (e.g. communication latency, bandwidth, achieved processing rate) serving as input. The model is used to provide insight into the achievable performance that should be possible on systems containing thousands of processors and to quantify the impact that possible improvements in sub-system performance may have. In addition, the impact on performance of modifying the communication structure of the code is also quantified.