This paper assesses the evolution of the distance to default during the recent crisis for some of the most traded companies on Bucharest Stock Exchange.The distance to default is formulated under the framework of the structural model of Leland (1994b) where the default threshold is endogenously determined. This model is reformulated as a (non-linear) state - space model where the (unobservable) state variable is the distance to default. After reviewing different methods proposed in the literature for estimation of the structural models, we estimate the model's parameters within the Bayesian approach with Markov Chain Monte Carlo (MCMC) methods.