Based on the observed equatorial ocean dynamic characteristics, the effects of a sloping thermocline and Rayleigh friction on the equatorially trapped free Kelvin waves were theoretically studied with a linear one and one half layer reduced gravity model, the multiple scale method and a small parameter expansion technique. Assuming that main thermocline depth (MTD) variations are slow, i.e. the changes of MTD over one wavelength are smaller than that of the wave amplitude and that wave reflections are negligible, the authors showed by their analytical results that the wavelengths and amplitudes of Kelvin waves are significantly modified by the MTD variations and Rayleigh friction. The results also showed that for an eastward shallowing thermocline, the zonal velocity of the Kelvin waves varies with thermocline depth to the power -7/8. The eastward shallowing of the thermocline depth strengthens Kelvin wave entrapment at the equator. Rayleigh friction reduces the Kelvin wave’s eastward velocity while the thermocline acts in the opposite way. The friction causes dispersion of the Kelvin wave, whose dissipation factor does not depend on its wavelength. The friction increases the lateral decay length and causes phase lines of Kelvin waves to slant westward in parabolic arcs. Based on the observed equatorial ocean dynamic characteristics, the effects of a sloping thermocline and Rayleigh friction on the equatorially trapped free Kelvin waves were theoretically studied with a linear one and one half layer reduced gravity model, the multiple scale method and a small parameter expansion technique Assuming that main thermocline depth (MTD) variations are slow, ie the changes of MTD over one wavelength are smaller than that of the wave amplitude and that wave reflections are negligible, the authors showed by their analytical results that the wavelengths and amplitudes of Kelvin waves are significantly modified by the MTD variations and Rayleigh friction. The results also showed that for an eastward shallowing thermocline, the zonal velocity of the Kelvin waves varies with thermocline depth to the power -7/8. The eastward shallowing of the thermocline depth strengthens Kelvin wave entrapment at the equator. Rayleigh friction reduces the Kelvin wave’s eastw ard velocity while the thermocline acts in the opposite way. The friction causes dispersion of the Kelvin wave, whose dissipation factor does not depend on its wavelength. The friction increases dispersion of the lateral decay length and causes phase lines of Kelvin waves to slant westward in parabolic arcs .