A theory of unsteady long waves in a stratified fluid over a channel of arbitrary cross section is proposed. The results obtained are general enough to meet any practical purpose, but rather simple in application. A formula is first derived to determine the wave speed in relation to any given density profile, current speed, and cross section of the channel. The wave form is then prescribed by a set of three time‐dependent equations, depending upon the relationship among the longitudinal length, wave amplitude, and time scales. The theory predicts the occurrence of various types of internal waves at the depth where the rate of change of the density profile is the largest in the increasing direction of depth, and with slight modification, the method developed is applied to the case of a fluid with infinite height or a fixed boundary, where density stratification plays an indispensable role.