The purpose of this report is to use the framework of hidden Markov chains for the modelling of the failure and debugging process of software, and the prediction of software reliability. The model parameters are estimated using the forward-backward EM algorithm and model selection is done with the BIC criterion. The advantages and drawbacks of this approach with respect to usual modelling are analyzed. Comparison is also done on real software failure data. The main contribution of hidden Markov chain modelling is that it highlights the existence of homogeneous periods in the debugging process, which allow one to identify major corrections or version updates. In terms of reliability predictions, the hidden Markov chain model performs well in average with respect to usual models, especially when the reliability is not regularly growing.