We explore the response of bedrock streams to eustatic and tectonically induced fluctuations in base level. A numerical model coupling onshore fluvial erosion with offshore wave‐base erosion is developed. The results of a series of simulations for simple transgressions with constant rate of sea‐level change (SLR) show that response depends on the relative rates of rock uplift (U) and wave‐base erosion (ɛ_w). Simple regression runs highlight the importance of nearshore bathymetry. Shoreline position during sea‐level fall is set by the relative rate of base‐level fall (U‐SLR) and ɛ_w, and is constant horizontally when these two quantities are equal. The results of models forced by a realistic Late Quaternary sea‐level curve are presented. These runs show that a stable shoreline position cannot be obtained if offshore uplift rates exceed ɛ_w. Only in the presence of a relatively stable shoreline position, fluvial profiles can begin to approximate a steady‐state condition, with U balanced by fluvial erosion rate (ɛ_f). In the presence of a rapid offshore decrease in rock‐uplift rate (U), short (∼5 km) fluvial channels respond to significant changes in rock‐uplift rate in just a few eustatic cycles. The results of the model are compared to real stream‐profile data from the Mendocino triple junction region of northern California. The late Holocene sea‐level stillstand response exhibited by the simulated channels is similar to the low‐gradient mouths seen in the California streams.