The linear instability of small but finite amplitude cnoidal waves on shallow water is examined. A new set of equations valid under the shallow water approximation is used to derive periodic wavetrains and to study the behavior of small perturbations. A resonance conditionk2 = k1 + 2k,similar to that used by other authors, is required to hold between the side‐band perturbations with wavenumbersk1andk2,and the main wave with wavenumberk.It is also necessary for the perturbations to have a specific nonzero frequency&OHgr;,measured with respect to the main wave which is stationary in a wave frame. In the region0 < F2 < 1,whereFis a Froude number of the flow underlying the cnoidal wave, all wavetrains are unstable to these side‐band perturbations. Like all other parametric instabilities, the instability is due to the resonant transfer of energy from the main wave to the perturbing waves.