Near a boundary in a rotating system, a Kelvin wave propagates with wave crests perpendicular to the side wall and wave height greatest at the side wall to the right of an observer looking in the direction of wave propagation. The wave height decreases exponentially from the side wall with e-folding length scale equal to the Rossby deformation radius c/f, in which f is the Coriolis parameter and c is the phase speed of the wave in the along boundary direction. In the shallow water approximation the waves are non-dispersive with frequency omega = +/- c k, in which k is the along boundary wavenumber and the phase speed c = (gH)^(1/2) with g the acceleration of gravity and H the mean fluid depth. Related to Kelvin waves in a channel are Poincare' waves.