Tree-based intercropping (TBI) may increase carbon (C) sequestration in agroecosystems, but may reduce crop yields. In this study of TBI, we used ecosys, a comprehensive mathematical model of terrestrial ecosystems, which represents interspecific competition for light, nutrients, and water, to evaluate the concurrent effects of TBI on C sequestration and crop yields in TBI experiments conducted at St. Paulin and St. Edouard in southern Quebec. Total gains in C sequestration vs. total losses in crop yields over 11 yr relative to monocropping were 682 vs. 396 g C m^-2 at St. Paulin and 841 vs. 168 g C m^-2 at St. Edouard. These gains and losses were generally consistent with the measurements at the two TBI sites and with those at TBI experiments under similar environmental conditions elsewhere. Gains and losses depended on competition for light by trees and crops, and so were affected by different fractions of tree foliage removal used to manage this competition in the model. The modelling protocol developed for this study provides a robust, process-based methodology to evaluate economic and environmental benefits of TBI under diverse climates, soils, and tree and crop management practices. Some of the key assumptions used to model TBI are also discussed.