Concentric tube robots are catheter-sized continuum robots that are well suited for minimally invasive surgery inside confined body cavities. These robots are constructed from sets of pre-curved superelastic tubes and are capable of assuming complex 3D curves. The family of 3D curves that the robot can assume depends on the number, curvatures, lengths and stiffnesses of the tubes in its tube set. The robot design problem involves solving for a tube set that will produce the family of curves necessary to perform a surgical procedure. At a minimum, these curves must enable the robot to smoothly extend into the body and to manipulate tools over the desired surgical workspace while respecting anatomical constraints. This paper introduces an optimization framework that utilizes procedureor patient-specific image-based anatomical models along with surgical workspace requirements to generate robot tube set designs. The algorithm searches for designs that minimize robot length and curvature and for which all paths required for the procedure consist of stable robot configurations. Two mechanics-based kinematic models are used. Initial designs are sought using a model assuming torsional rigidity. These designs are then refined using a torsionally-compliant model. The approach is illustrated with clinically relevant examples from neurosurgery and intracardiac surgery.