A theoretical examination is made of the problem of the electromagnetic fields of electric dipoles in the presence of an infinitely long, perfectly conducting cylinder. Application of the Green's function method to this problem yields expressions for the fields in terms of an integration in the complex plane. Simplified expressions for far zone fields are obtained through the known result of the complex integration for the far zone conditions. Results are given for both circular and elliptic cylinders. In the latter case, it is possible to treat the problem of dipoles in the presence of a ground plane which is finite in one dimension and infinite in the other, since this is equivalent to an elliptic cylinder with a vanishing minor axis. Polar diagrams of calculated far zone fields are included for a number of cases.