In this paper we propose a stochastic formulation of the materials balance condition which imposes physical constraints on production technologies. The estimation of the model involves a composed error term structure that is commonly applied in the literature on stochastic frontier analysis of productive efficiency. Moreover, we discuss how OLS, maximum likelihood and Bayesian methods can be used to estimate the proposed model. In contrast to previous approaches our model allows to estimate the physical limitations to production possibilities in the presence of statistical noise and depends on substantially weaker data requirements. We demonstrate the applicability of our new approach by estimating the materials balance condition for SO2 and CO2 using a sample of fossil-fueled power plants in the United States.