A three‐dimensional physically based stochastic model was developed to describe canopy rainfall interception processes at desired spatial and temporal resolutions. Such model development is important to understand these processes because forest canopy interception may exceed 59% of annual precipitation in old growth trees. The model describes the interception process from a single leaf, to a branch segment, and then up to the individual tree level. It takes into account rainfall, meteorology, and canopy architecture factors as explicit variables. Leaf and stem surface roughness, architecture, and geometric shape control both leaf drip and stemflow. Model predictions were evaluated using actual interception data collected for two mature open grown trees, a 9‐year‐old broadleaf deciduous pear tree (Pyrus calleryana “Bradford” or Callery pear) and an 8‐year‐old broadleaf evergreen oak tree (Quercus suber or cork oak). When simulating 18 rainfall events for the oak tree and 16 rainfall events for the pear tree, the model over estimated interception loss by 4.5% and 3.0%, respectively, while stemflow was under estimated by 0.8% and 3.3%, and throughfall was under estimated by 3.7% for the oak tree and over estimated by 0.3% for the pear tree. A model sensitivity analysis indicates that canopy surface storage capacity had the greatest influence on interception, and interception losses were sensitive to leaf and stem surface area indices. Among rainfall factors, interception losses relative to gross precipitation were most sensitive to rainfall amount. Rainfall incident angle had a significant effect on total precipitation intercepting the projected surface area. Stemflow was sensitive to stem segment and leaf zenith angle distributions. Enhanced understanding of interception loss dynamics should lead to improved urban forest ecosystem management.