Microsatellites are simple sequence repeats present in both coding and non-coding regions of the genome. DNA instability at some microsatellites is the underlying genetic defect in a number of human diseases including myotonic dystrophy type 1 (DM1). New quantitative data, collected by single molecule analysis of repeat length in blood cells from 145 DM1 patients reveals the extent and nature of the genetic variation within and between patients (Morales, PhD thesis, 2006). This dataset of thousands of de novo mutations provides a unique opportunity to examine the underlying mechanism of mutation, which is thought to be a universal biological process that is simply amplified in the disease case. We are developing discrete mathematical models and stochastic simulation techniques that capture key features of the mutation mechanism underlying repeat length evolution. We derive analytical expressions for the length distribution of an adapted birth and death process and employ Bayesian techniques to calibrate our models against the biological data and test model hypotheses. Our work aims to improve prognostic information for patients, as well as providing a deeper understanding of the underlying biological process. In particular we will provide evidence that a previous model (Kaplan et al., 2007) can be improved by introducing a non-zero contraction rate.