This article estimates behavioural parameters of the quadratic regional supply models in the modelling system CAPRI. Using the time-series data in the CAPRI database, we directly estimate the optimality conditions using a Bayesian highest posterior density estimator. After discarding regions with insufficient data, parameters for up to 23 crop production activities with related inputs, outputs, prices and behavioural functions are estimated for 219 regions in EU-27. The results are systematically compared with the outcomes of other studies. For crop aggregates (e.g. cereals, oilseeds, etc.) at the national level, the estimated own price elasticities of supply are found to be in a plausible range. On a regional level and for individual crops, the picture is much more diverse. As far as we know, there is no other study of similar regional and product coverage.