The primary objective of this paper is to estimate behavioural parameters of the quadratic regional supply models in the modelling system CAPRI, using the time series data in the CAPRI database. A secondary objective is to replace the constant yields of the original model by functions that depend on input use. Due to lack of statistical robustness, the second objective is not achieved, thus yields remain constant. A Bayesian highest posterior density estimator is developed to address the primary objective. 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 165 regions in EU-15. The results are systematically compared to the outcomes of other studies. For crop aggregates (e.g. cereals, oilseeds etc.) on the level of nations, 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. Whether the regional results are plausible or not is difficult to judge, since no other study of similar regional and product coverage is known to the author.