This paper examines supply response models in a rational expectations framework for each one of the four major Greek meat markets, i.e. beef, broiler, lamb and pork. A multivariate GARCH model with Cholesky decomposition is used to incorporate price volatility into the rational expectations supply response model for each meat category and as a result the conditional covariance matrix remains positive definite without imposing any restrictions on the parameters. The empirical results confirm the existence of rational behaviour by meat producers in the four examined markets and indicate that price volatility is a major risk factor in Greek meat production while feed prices and veterinarian medicine prices are both important cost factors. Furthermore, the last Common Agricultural Policy reform is found to have a negative impact on the beef and lamb production in Greece.