Sheep farming is an important agricultural activity in Greece, since it contributes highly in the country’s gross agricultural production value. Recently, sheep milk production received further attention because of the increased demand for feta cheese and also because of the excessive price level suffered by the consumers, in contrast with the prices paid at the farm level. In this study, we suggest the use of multicriteria analysis to estimate the supply response of sheep milk to price. The study focuses in the Prefecture of Etoloakarnania, located in Western Greece, where sheep farming is a common and traditional activity. A non-interactive technique is used to elicit farmers’ individual utility functions which are then optimized parametrically subject to technico-economic constraints, to estimate the supply function of sheep milk. Detailed data from selected farms, representing different farm types and management strategies, have been used in the analysis. The results indicate that the multicriteria model reflects the actual operation of the farms more accurately than the gross margin maximization model and therefore leads to a more robust estimation of the milk supply.