The performance of unstructured mesh applications presents a number of complexities and subtleties that do not arise for dense structured meshes. From a programming point of view, the handling of unstructured meshes has an increased complexity in order to manage the necessary data structures and interactions between mesh-cells. From a performance point of view, there are added difficulties in understanding both the processing time on a single processor and the scaling characteristics when using large-scale parallel systems. In this work we present a general performance model for the calculation of deterministic S_N transport on unstructured meshes that is also applicable to structured meshes. The model captures the key processing characteristics of the calculation and is parametric using both system performance data (latency, bandwidth, processing rate etc.) and application data (mesh size etc.) as input. A single formulation of the model is used to predict the performance of two quite different implementations of the same calculation. It is validated on two clusters (an HP AlphaServer and an Itanium-2 system) showing high prediction accuracy.