The growing demand for sustainable agriculture is raising interest in intercropping for its multiple potential benefits to avoid or limit the use of chemical inputs or increase the production per surface unit. Predicting the existence and magnitude of those benefits remains a challenge given the numerous interactions between interspecific plant-plant relationships, their environment, and the agricultural practices. Soil-crop models are critical in understanding these interactions in dynamics during the whole growing season, but few models are capable of accurately simulating intercropping systems. In this study, we propose a set of simple and generic formalisms (i.e. the structure and mathematical representation necessary for designing a model) for simulating key interactions in bi-specific intercropping systems that can be readily included into existing dynamic crop models. This requires simulating important processes such as development, light interception, plant growth, N and water balance, and yield formation in response to management practices, soil conditions, and climate. These formalisms were integrated into the STICS soil-crop model and evaluated using observed data of intercropping systems of cereal and legumes mixtures, including Faba bean-Wheat, Pea-Barley, Soybean-Sunflower, and Wheat-Pea mixtures. We demonstrate that the proposed formalisms provide a comprehensive simulation of soil-plant interactions in various types of bispecific intercrops. The model was found consistent and generic under a range of spring and winter intercrops (nRMSE = 25% for maximum leaf area index, 23% for shoot biomass at harvest, and 18% for grain yield). This is the first time a complete set of formalisms has been developed and published for simulating bi-specific intercropping systems and integrated into a soil-crop model. With its emphasis on being generic, sufficiently accurate, simple, and easy to parameterize, STICS is well-suited to help researchers designing in silico