Linear stability of zonal jets in a shallow water system on a f-plane is investigated, and the stability characteristics are compared with those obtained in a quasi-geostrohie system for a wide range of Rossby number Ro, and Froude number Fr. The maximum growth rates are similar value in both systems for a wide parameter range; even for high Ro with small Fr. On the other hand, unstable modes in a shallow water system have asymmetry with respect to the center of the jet for high Ro. owing to asymmetry in the surface displacement of the basic state. This asymmetric property is explained by dividing the dependent variables into symmetric and asymmetric components in the linearized equations.