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Linear-/circular-polarization designs of the dual-/wide-band cylindrical dielectric resonator antennas (DRAs) are presented. The HEM111 and HEM113 modes of the cylindrical DRA are utilized to design the dual-mode cylindrical DRA. A wideband antenna can be obtained by merging the two resonant modes. To facilitate the designs, new engineering formulas that determine the dimensions of the dual-mode cylindrical DRA are found for the first time. They are obtained by using the covariance matrix adaptation evolutionary strategy (CMA-ES). Design examples for the dual-/wide-band cylindrical DRAs are given for both the linearly and circularly polarized cases. Ansoft HFSS was used to simulate the DRAs and the simulations were verified with our measurements. Good agreement between the measured and simulated results is observed.