A systematic approach is presented for the design of profiled dielectric rod antennas that satisfy specified radiation pattern objectives. The approach uses a body of revolution method of moments technique to rapidly analyze arbitrarily profiled dielectric rods while a genetic algorithm is used to achieve the design objectives. As examples we present dielectric rod designs optimized for maximum gain and low sidelobes. These designs are compared with a conventional linear profile design. Measured results are presented and these are shown to agree well with the calculated radiation patterns. We show that improved gain and sidelobe performance is achieved using a non-linear rod profile compared to a standard linear profile. The generality of the approach is demonstrated with a shaped beam antenna design that has a cosecant-squared pattern.