Most of existing works on the tubes design optimization of concentric-tube robot (CTR) do not include the elastic stability in the optimization criteria. The only work which formulates the elastic stability in the objective function is based on scalarization method which is used in existing multi-objective design optimization. The objective function is formed by a set of weighted objective functions. The selection of the weights is crucial as the optimization results are greatly affected by them and could be misleading if these weights are improperly chosen. As an alternative optimization technique, we use Pareto grid-searching method to avoid this problem and allow a straightforward interpretation of the results following the selection criteria for the parameters to be optimized. This paper shows a three-tube CTR design based on Pareto grid-searching method in order to optimize the reachability and elastic stability of the CTR within a specific curvature range dedicated to the deep anterior brain tumor removal surgery.