© 2022 IEEE.Cavity resonators are useful devices of microwave and optical systems. Behavior of the cavity resonators at their resonance frequencies is a very well-known topic. However, at low frequencies below the first resonance frequency, there are very few studies for the cavity resonators. To the best of our knowledge, there is no full wave analytical or numerical solution to a lossy dielectric filled cavity resonator excited below its first resonance frequency. In this study, first, a field distribution of an empty rectangular cavity resonator excited below the frequencies of the first resonance is calculated by using finite difference time domain (FDTD) method. The results are validated with an analytical solution. Afterwards, the field distribution of the same cavity resonator filled with the lossy dielectric is calculated by using a Quasi-Static FDTD (QS-FDTD) method below the frequency of the first resonance.