Summary: The software package Prometheus is Canada’s only operational wildfire growth modelling simulator. The program calculates accurate, fast, multi-day forecasts of moving fire fronts and is currently used in fire fighting situations, in fire risk analysis and in the design of “fire-safe” communities and forests. At the core of Prometheus is an algorithm that calculates the evolution of the fire front in an empirical manner, assuming locally elliptic fire spread and Huygens’ principle in a Lagrangian description of the evolution. This report describes progress made on a set of problems that Prometheus developers brought to the 10th Pacific Institute for the Mathematical Sciences (PIMS) Industrial Problem Solving Workshop held in June 2006 at Simon Fraser University. In particular, we investigate the mathematical background behind the Prometheus code and suggest a new method (the “outer hull” approach) to remove tangles from the evolving front. Other methods that can reduce tangles and crossings are “smoothing” of data and parameters, and redistribution of vertices on the evolving front. We investigate the use of de Boor’s algorithm as an automated procedure for redistributing vertices along the front. Finally, we investigate the level set method as a new tool for forest fire spread simulations and show in some simple test cases the excellent potential of this method.