This paper describes the analysis of a hemispherical dielectric resonator antenna fed by a coaxial probe. The electric field Green's function of a vertical point current located inside the dielectric hemisphere is derived by mode matching technique. Delta gap source excitation model is employed. The input impedance of the antenna is calculated using a variational formula. Both the broadside TE111 mode (the lowest-order transverse electric mode) and the end-fire TM101 mode (the lowest-order transverse magnetic mode) are considered. Numerical calculations and experimental results validating the theory are shown. The variation of input resistance with dielectric constant of the antenna is studied.