The fundamental properties of carbon nanotube straight wire antennas were determined using theoretical and numerical modelling. The reflection coefficient, radiation efficiency and Q-factor have been reported using classical Hallén's-type integral equation, based on quantum mechanical conductivity. Contrary to the ordinary metal antennas with dimensions less than 0.01 m, the addition of parasitic elements in a Yagi-Uda antenna with carbon nanotubes does not lead to significant changes in the radiation characteristics as the induced current in the parasitic elements is small. The radiation efficiency of the Yagi-Uda antenna shows little change. The Q-factor limited by radiation efficiency was compared to the fundamental limits proposed by Chu and Thal. Although the Q-factor of modelled nanotube antennas is very small, it is still larger than the fundamental limits proposed by Chu and Thal.