The purpose of this research is to find ways to create an omnidirectional antenna with high directivity in the vertical plane. The investigation is based on computer simulation using the program CST 2011. The objective is a narrow-band antenna that is omnidirectional in the horizontal plane and has maximum achievable directivity for a fixed size. Three of the most promising antenna designs are selected based on the current state of antenna technology. Their maximum directivities are estimated by means of well known relations in antenna theory. It is shown that the most suitable design is an omnidirectional antenna in the form of a cylindrical dipole antenna array with an active central dipole. For this antenna, excitation by means of a radial traveling wave, with a phase velocity smaller than speed of the light, is possible. It is found that for a certain value of a moderating factor it is possible to obtain a directivity that is 2.5 – 3 dB larger than that of a dipole or a linear antenna with uniform excitation. The antenna structures are modeled to determine the number of dipoles, their dimensions and the spacing between them that maximizes the directivity.