Interactions between food demand, biomass energy and forest preservation are driving both food prices and land-use changes, regionally and globally. This study presents a new model called Nexus Land-Use which describes these interactions through a generic representation of agricultural intensification mechanisms. The Nexus Land-Use model equations combine biophysics and economics into a single coherent framework to calculate crop yields, food prices, and resulting pasture and cropland areas within 12 regions inter-connected with each other by international trade. The representation of cropland and livestock production systems in each region relies on three components: (i) a biomass production function derived from the crop yield response function to inputs such as industrial fertilisers ; (ii) a detailed representation of the livestock production system subdivided into an intensive and an extensive component, and (iii) a spatially explicit distribution of potential (maximal) crop yields prescribed from the Lund-Postdam-Jena global vegetation model for managed Land (LPJmL). The economic principles governing decisions about land-use and intensification are adapted from the Ricardian rent theory, assuming cost minimisation for farmers. The land-use modelling approach described in this paper entails several advantages. Firstly, it makes it possible to explore interactions among different types of demand for biomass for food and animal feed, in a consistent approach, including indirect effects on land-use change resulting from international trade. Secondly, yield variations induced by the possible expansion of croplands on less suitable marginal lands are modelled by using regional land area distributions of potential yields, and a calculated boundary between intensive and extensive production. The model equations and parameter values are first described in detail. Then, idealised scenarios exploring the impact of forest preservation policies or rising energy price on agricultural intensification are described, and their impacts on pasture and cropland areas are investigated.