We develop a simple stochastic theory for erosion and sediment transport, based on the Poisson pulse rainfall model, in order to analyze how variability in rainfall and runoff influences drainage basin evolution. Two cases are considered: sediment transport by runoff in rills and channels and particle detachment from bedrock or cohesive soils. Analytical and numerical results show that under some circumstances, rainfall variability can have an impact equal to or greater than that of mean rainfall amount. The predicted sensitivity to rainfall variability is greatest when (1) thresholds for runoff generation and/or particle detachment are significant and/or (2) erosion and transport are strong nonlinear functions of discharge. In general, sediment transport capacity is predicted to increase with increasing rainfall variability. Depending on the degree of nonlinearity, particle detachment capacity may either increase or decrease with increasing rainfall variability. These findings underscore the critical importance of hydrogeomorphic thresholds and other sources of nonlinearity in process dynamics. The morphologic consequences of rainfall variability are illustrated by incorporating the pulse rainfall theory into a landscape simulation model. The simulation results imply that, all else being equal, catchments experiencing a shift toward greater climate variability will tend to have (1) higher erosion rates, (2) higher drainage density (because of increased runoff erosion efficiency), and ultimately (3) reduced relief. The stochastic approach provides a useful method for incorporating physically meaningful climate data within the current generation of landscape evolution models.