The tip of a flexible needle with a bevel tip approximately follows a planar arc when it is inserted into soft tissue only with the force applied to the needle along the needle axis. The direction of the arc can be controlled by the rotation input around the needle axis. This flexible and steerable needle has been shown to have a considerable potential in clinical applications due to its maneuverability and steerability. Beyond the needle insertion to a single destination, this paper concerns obtaining needle trajectories that reach multiple targets. Specifically, we propose an algorithm for the insertion of a flexible needle to travel from a single insertion point (i.e. port) to multiple targets. The insertion is motivated by the observation that multiple targets can be reached by the flexible needle through a combination of insertion, partial retraction, turning, and reinsertion of the flexible needle. In this paper we develop an insertion algorithm that minimizes tissue damage during the needle insertion to multiple targets. To this end, a cost function which computes the length of needle trajectory that can be thought of as the tissue damage is defined, and is minimized. Through the minimization, we find the optimal insertion parameters such as the port location, the insertion direction at the port, the targeting order, the turning angles, and the lengths of forward insertions and retractions. To reduce the computation time, we perform workspace analysis for this approach to filter out the no-solution cases. We present numerical examples of the simulated needle insertion for multiple targets with and without obstacles and show the benefit of the proposed method in terms of the tissue damage and the number of skin punctures. Extensions of the proposed approach to more complex cases such as more than three target points and maneuvering around spherical obstacles are also discussed.