Several basal theoretical problems for the radiation of plasma antenna are investigated. The system equations are obtained according to the rule of the disturbing current, which is excited by surface waves on the interface between a plasma column and a dielectric tube, and the radiation theory of dielectric antennae. The analysis indicates that there are two kinds of mechanisms to explain the radiation of plasma antennae. The first one is the radiation of the disturbing current, which is similar to the radiation of a metal antenna. In the second case, because the electromagnetic wave partly cannot satisfy the total reflection condition in some specific frequency bands, transmission can be excited in a plasma antenna, which is similar to the radiation of a dielectric antenna. The radiation derived from these two kinds of mechanisms can be superposed in certain frequency bands. In this paper, a radiation directivity function is obtained. The radiation characteristics of plasma antennae are compared with those of metal antennae. The radiation properties of plasma antennae are presented based on numerical calculation. The present results provide an important theory for further investigation in the performance of controlling plasma antennae and plasma antenna arrays.