The analysis of fission tracks found in minerals can yield geological information valuable for a range of applications (particularly in oil exploration). This work presents and explains a "line segment" model of fission track analysis that represents fission tracks mathematically by a stochastic process of randomly oriented line segments in three dimensions. Author Galbraith (statistical science, U. College London, UK) also explores the model's practical applications for statistical analysis and modeling, including statistical analysis of fission track dating using the external detector and population methods, statistical modeling of mixed fission track ages, probability distributions relevant to length and angle measurements, empirical features of such measurements, and the statistical basis of annealing models and thermal histories (detailed discussion of which is left for elsewhere, being beyond the scope of this work).