Using exact numerical methods for finite-size nonplanar objects, we demonstrate a stable mechanical suspension of a Silica cylinder within a metallic cylinder separated by Ethanol, via a repulsive Casimir force between the Silica and the metal. We investigate cylinders with both circular and square cross sections, and show that the latter exhibit a stable orientation as well as a stable position, via a method to compute Casimir torques for finite objects. Furthermore, the stable orientation of the square cylinder is shown to undergo an unusual 45 degree transition as a function of the separation length-scale, which is explained as a consequence of material dispersion.