Abstract. A fast scheme is described to compute the 3-D interaction of solar radiation with vegetation canopies. The canopy is split in the horizontal plane into one clear region and one or more vegetated regions, and the two-stream equations are used for each, but with additional terms representing lateral exchange of radiation between regions that are proportional to the area of the interface between them. The resulting coupled set of ordinary differential equations is solved using the matrix-exponential method. The scheme is compared to solar Monte Carlo calculations for idealized scenes from the RAMI4PILPS intercomparison project, for open forest canopies and shrublands both with and without snow on the ground. Agreement is good in both the visible and infrared: for the cases compared, the root-mean-squared difference in reflectance, transmittance and canopy absorptance is 0.020, 0.038 and 0.033, respectively. The technique has potential application to weather and climate modelling.