Tne main goal of the paper is to discriminate among stochastic frontier cost functions. The unknown cost function is approximated by the locally flexible functional forms: the translog, generalised Leontoef and McFadden and two non-flexible forms: the Cobb-Douglas model with varying returns to scale and the Cobb-Douglas model with the Muentz-Schatz series expansion of order one for the price aggregator. Numerical approximations of moments of marginal posterior distributions are accomplished by implementation of the Markov Chain Monte Carlo techniques, that is the Metropolis-Hastings algorithms within Gibbs sampling. Marginal data density is obtained on the basis of the S. Chib's method proposed in 1995. Detailed discussion of specification of the prior distribution for the technology parameters with the posterior sensitivity analysis is included in the paper. After assuming the same prior standard deviation for the technology parameters in each model the authoress concludes that ther most probable a posteriori is the translog model, whose posterior probability is almost equal to one. The generalised Leontief and McFadden flexible forms are equally probable and are much more supported by the data than the non-flexible forms, such as the Cobb-Douglas. The ranking of models does not change when the dispersion of the prior distribution of technology parameters increases evenly but it can be noticed that the marginalised likelihood drops slightly faster for the Generalised McFadden model than for the Generalised Leontief and Muentz-Szatz series expansions of order one. After assuming the same marginal prior distribution of all individual technology parameters in each model the posterior model probabilities are not affected by the prior model probabilities. The marginal posterior distribution of technology characteristics and the cost efficiency, weighted by the posterior model probabilities, would be equal to the one obtained according to translog.