In spite of the economic importance and extensive agronomic literature on cocoa, no physiological production model has been developed for cocoa so far. Such a model would be very useful to compare yields in different climates and cropping systems, and to set the agenda for future agronomic research. Here, we present and apply such a physiological growth and production model for cocoa (SUCROS-Cocoa), based on the SUCROS-family of physiological crop growth models. Our model calculates light interception, photosynthesis, maintenance respiration, evapotranspiration, biomass production and bean yield for cocoa trees grown under shade trees. It can cope with both potential and water-limited situations, and is parameterised using existing information on cocoa physiology and morphology. A validation study showed that the model produces realistic output for bean yield, standing biomass, leaf area and size-age relations. Simulations were carried out using climatic information of 30 locations in 10 cocoa-producing countries, three different soil types and varying shade levels. The model was applied to answer four questions that are currently relevant to cocoa production. (1) Which are the most important yield-determining parameters? Sensitivity analyses revealed that these parameters were chiefly related to the morphology of fruits, photosynthesis and maintenance respiration. (2) To what extent can cocoa yield be predicted by rainfall and irradiance data? Regression analyses showed that over 70% of the variation in simulated bean yield could be explained by a combination of annual radiation and rainfall during the two driest months. (3) How large is the cocoa yield gap due to water limitation? Yield gaps were large - up to 50% - for locations with a strong dry season combined with an unfavourable (clayey or sandy) soil. The calculated yield gaps decreased exponentially with the amount of rain during the two driest months. (4) What are the consequences of shading on cocoa yield? Our simulations showed that moderate shade levels hardly affected bean yield, whereas heavy shading (>60%) reduced yields by more than one-third.