We compute the Casimir energy for two perfectly conducting, infinite, concentric cylinders. We first obtain the zero point electromagnetic energy using a semiclassical approximation that takes into account families of classical periodic orbits that reflect off both cylinders. Then we compute the exact energy using the mode-by-mode summation technique based on Cauchy's theorem. We analyze the validity of the semiclassical approximation and show that it improves the results obtained through the proximity theorem.