Abstract: Based on a shallow waster model on the equatorial beta-plane, theoretical analysises were carried out. Firstly, we analytically abtained linear free-wave solutions and found that for the solutions of the lowest modes the symmetry or antisymmetry of u, φ and that of v are just the opposite. Secondly, we used a highly truncated spectral model to analyse the equilibria in the tropical circulations induced by idealized diabatic heating sources. It was found that there exist two different steady equilibrium states in the summer, but exists one in the winter.