This paper presents a theoretical model of the rectangular-shaped microstrip patch antennas on liquid crystal (LC) substrates in order to accurately derive the resonant frequencies and radiation performances. The model is based on the solution of the mode matching about an LC loaded cavity. The calculation results of the theoretical model are compared with the experiment and simulation results. The discrepancy between calculation and simulation results is merely 2.7%. In addition, a tuning mechanism of the patch antenna on the LC substrate is verified depending on the strength of a biasing voltage. The calculated results of the theoretical model indicate that the resonant frequency is shifted toward lower direction and 3-dB beamwidth of radiation pattern increases as the bias voltage increases. Although the calculated maximum directivity decreases with the increment of voltage, the realized gain increases due to the radiation efficiency of the antenna.