A neighbourhood-scale multi-layer urban canopy model of shortwave and longwave radiation exchange that explicitly includes the radiative effects of tall vegetation (trees) is presented. Tree foliage is permitted both between and above buildings, and mutual shading, emission and reflection between buildings and trees are included. The basic geometry is a two-dimensional canyon with leaf area density profiles and probabilistic variation of building height. Furthermore, the model accounts for three-dimensional path lengths through the foliage. Ray tracing determines the receipt of direct shortwave irradiance by building and foliage elements. View factors for longwave and shortwave diffuse radiation exchange are computed once at the start of the simulation using a Monte Carlo ray tracing approach; for subsequent model timesteps, matrix inversion rapidly solves infinite reflections and interception of emitted longwave between all elements. The model is designed to simulate any combination of shortwave and longwave radiation frequency bands, and to be portable to any neighbourhood-scale urban canopy geometry based on the urban canyon. Additionally, the model is sufficiently flexible to represent forest and forest-clearing scenarios. Model sensitivity tests demonstrate the model is robust and computationally feasible, and highlight the importance of vertical resolution to the performance of urban canopy radiation models. Full model evaluation is limited by the paucity of within-canyon radiation measurements in urban neighbourhoods with trees. Where appropriate model components are tested against analytic relations and results from an independent urban radiation transfer model. Furthermore, system response tests demonstrate the ability of the model to realistically distribute shortwave radiation among urban elements as a function of built form, solar angle and tree foliage height, density and clumping. Separate modelling of photosynthetically-active and near-infrared shortwave bands is shown to be important in some cases. Increased canyon height-to-width ratio and/or tree cover diminishes the net longwave radiation loss of individual canyon elements (e.g., floor, walls), but, notably, has little effect on the net longwave loss of the whole urban canopy. When combined with parametrizations for the impacts of trees on airflow and hydrological processes in the urban surface layer, the new radiation model extends the applicability of urban canopy models and permits more robust assessment of trees as tools to manage urban climate, air quality, human comfort and building energy loads.