The theoretical model of an insulated antenna in a general ambient medium is reviewed briefly. Attention is then directed to the solution of the integral equation for the current distribution in the antenna. The properties of the kernel are discussed in detail, and approximate solutions for the complex wave number are obtained. The evaluation of the kernel and other related numerical problems are discussed and a numerical method of computation is presented. A discussion of approximate solutions is included. A comparison of the theoretical results with measured data and numerical computations is made to check the applicable range of the theory.