Laser drilling is very important in many industries such as automotive, aerospace, electronics, and materials processing. It can be used to produce critical components with novel hole geometry for advanced systems. Percussion drilling and trepanning are two laser drilling methods. In the conventional trepanning method, a laser beam is scanned along a circular or spiral orbit to remove material to achieve a desired hole shape. These orbits generally trace a circular path at the inner wall of the holes. This suggests that an annular beam can be used to accomplish trepanning, a technique we refer to as optical trepanning. The ray-tracing technique of geometrical optics is employed in this paper to design the necessary optics to transform a Gaussian laser beam into an annular beam of different intensity profiles. Such profiles include uniform intensity within the annulus, full Gaussian with maximum intensity, and half Gaussian with maximum intensities at the inner and outer surfaces of the annulus.