Design of the dualband rectangular dielectric resonator antenna is presented. The fundamental TE111y mode and higher-order TE113y mode are used for the design, with their resonance frequencies controlled by changing the DRA dimensions. In this paper, the dielectric waveguide model (DWM) is used to calculate the resonance frequencies of the two modes. To demonstrate the idea, a dualband DRA for WiMAX and WLAN applications is designed. The reflection coefficient, radiation pattern, and antenna gain of the dualband DRA were simulated using Ansoft HFSS, and good agreement between the predicted and simulated resonance frequencies is obtained.