We present sea level spectra computed from bottom pressure records at two locations around the Balearic Islands, Western Mediterranean. In these spectra, several sea level oscillation peaks are observed at both sides of Mallorca Island. Moreover, the relative magnitudes of the first two peaks switch during the rissaga events. To understand the appearance of these modes and their changes during 'rissaga', a simple analytical model is presented for atmospheric pressure induced edge waves on a circular shelf with a circular island in the middle. The analytical solutions indicate that indeed the peaks in the observed spectra can be identified as the fundamental modes of the edge waves. The analytical solutions also confirm that the magnitude of the second peak becomes higher than the first peak only when the phase speed of the atmospheric pressure waves become almost the same as that of the long ocean wave on the Mallorca shelf.