The rivr package provides a computational toolset for simulating steady and unsteady one-dimensional flows in open channels. It is designed primarily for use by instructors of undergraduate- and graduate-level open-channel hydrodynamics courses in such diverse fields as river engineering, physical geography and geophysics. The governing equations used to describe open-channel flows are briefly presented, followed by example applications. These include the computation of gradually-varied flows and two examples of unsteady flows in channels-namely, the tracking of the evolution of a flood wave in a channel and the prediction of extreme variation in the water-surface profile that results when a sluice gate is abruptly closed. Model results for the unsteady flow examples are validated against standard benchmarks. The article concludes with a discussion of potential modifications and extensions to the package.