Dependability evaluation is a basic component in the assessment of the quality of repairable systems. We develop here a general model specifically designed for software systems that allows the evaluation of different dependability metrics, in particular, of availability measures. The model is of the structural type, based on Markov process theory. In particular, it can be viewed as a attempt to overcome some limitations of the well-known Littlewood's reliability model for modular software. We give both the mathematical results necessary to the transient analysis of this general model and the algorithms that allow to evaluate it efficiently. More specifically, from the parameters describing : the evolution of the execution process when there is no failure, the failure processes together with the way they affect the execution, and the recovery process, we obtain the distribution function of the number of failures on a fixed mission period. In fact, we obtain dependability metrics which are much more informative than the usual ones given in a white-box approach. We briefly discuss the estimation procedures of the parameters of the model. From simple examples, we illustrate the interest in such a structural view and we explain how to take into account reliability growth of part of the software with the transformation approach developed by Laprie and al. Finally, the complete transient analysis of our model allows to discuss in our context the Poissonian approximation reported by Littlewood for its model.