A partial differential equation for the adjusted sea level, obtained from the long wave equations in shallow water, is reduced to a simpler one by the use of physically reasonable approximations based on the observations. The similar equation for the stream function indicates that shelf waves are generated by the longshore wind stress. This indication is in good agreement with the high correlation between the adjusted sea levels and the longshore wind stress. From the dispersion relationship and the boundary conditions, there exist a countable infinite number of modes which satisfy a first-order wave equations. The adjusted sea level for a given wind stress can easily be calculated by utilizing the convolution and the Fourier transformation. Some detailed solutions are presented here for sinusoidal and exponential wind stress.