This paper deals with the analytical and numerical approaches used to estimate the natural frequencies of circular plates in contact with a liquid. The circular plate is assumed to be in contact with a liquid on one side and placed into the hole of an infinite rigid wall; this is the problem studied by Lamb. The change in natural frequencies is first calculated using the so-called nondimensional added virtual mass incremental (NAVMI) factor which reflects the increase of kinetic energy due to the liquid. The analytical expression of NAVMI factors for circular plates possessing axisymmetric boundary conditions is obtained. The more accurate Rayleigh-Ritz solution of the problem is then taken and compared to the results obtained by using the NAVMI factors. Numerical data is given for both free-edge, simply supported and clamped plates and for supported plates with an elastic moment edge constraint.