We consider the problem of optimally covering solid bodies by a given number of spheres. The mathematical modeling of this problem leads to a min-max-min formulation which, in addition to its intrinsic multilevel nature, has the significant characteristic of being nondifferentiable. In order to overcome these difficulties, we have developed a smoothing strategy using a special class C∞ smoothing function. The final solution is obtained by solving a sequence of differentiable subproblems which gradually approach the original problem. The use of this technique, called Hyperbolic Smoothing, allows the main difficulties presented by the original problem to be overcome. A simplified algorithm containing only the essential of the method is presented. For the purpose of illustrating both the actual working and the potentialities of the method, a set of computational results is presented.