We present the simulation and design of an antenna system for a borehole radar. To obtain a directional radiation pattern the transmitting dipole is shielded with a reflector. The generated transient wavefield, with a centre frequency of 100 MHz, is reflected in the desired direction by a perfectly conducting cylindrically curved plate. The radiation pattern of this scattered wavefield is computed by solving the integral equation for the unknown electric surface current at the reflector. The reflector can have either a circular cylindrical shape or a parabolic cylindrical shape. Once the electric current distributions at the dipole and the reflector are known, the radiated wavefield can be represented by an integral over the wire and the curved plate. A prototype has been built and the simulated data are compared with experimental results.