Within a channel in a rotating system, a Poincare' wave has sinusoidally varying cross-channel velocity with an integral or half integral number of cross-channel waves spanning the channel. In the shallow water approximation the waves have dispersion relationship with squared frequency omega^2 = f^2 + c^2 (k^2 + n^2 pi^2/L^2), in which f is the Coriolis parameter, k is the along channel wavenumber, L is the width of the channel, n is any positive integer, and c is the phase speed for shallow water gravity waves: c=(gH)^(1/2), in which g is the acceleration due to gravity and H is the mean depth of the fluid. Related to Poincare' waves are Kelvin waves which take the role of the mode with n=0.