In small and intermediate sized streams, the interaction between wood and bed material transport often determines the nature of the physical habitat, which in turn influences the health of the stream's ecosystem. We present a stochastic model that can be used to simulate the effects on physical habitat of forest fires, climate change, and other environmental disturbances that alter wood recruitment. The model predicts large wood (LW) loads in a stream as well as the volume of sediment stored by the wood; while it is parameterized to describe gravel bed streams similar to a well-studied field prototype, Fishtrap Creek, British Columbia, it can be calibrated to other systems as well. In the model, LW pieces are produced and modified over time as a result of random tree-fall, LW breakage, LW movement, and piece interaction to form LW jams. Each LW piece traps a portion of the annual bed material transport entering the reach and releases the stored sediment when the LW piece is entrained and moved. The equations governing sediment storage are based on a set of flume experiments also scaled to the field prototype. The model predicts wood loads ranging from 70 m3/ha to more than 300 m3/ha, with a mean value of 178 m3/ha: both the range and the mean value are consistent with field data from streams with similar riparian forest types and climate. The model also predicts an LW jam spacing that is consistent with field data. Furthermore, our modeling results demonstrate that the high spatial and temporal variability in sediment storage, sediment transport, and channel morphology associated with LW-dominated streams occurs only when LW pieces interact and form jams. Model runs that do not include jam formation are much less variable. These results suggest that river restoration efforts using engineered LW pieces that are fixed in place and not permitted to interact will be less successful at restoring the geomorphic processes responsible for producing diverse, productive physical habitats than efforts using LW pieces that are free to move, interact, and form LW jams.