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Steerable needles composed of a highly flexible material and with a bevel tip offer greater mobility compared to rigid needles for minimally invasive medical procedures. In this paper, we apply sampling-based motion planning technique to explore motion planning for the steerable bevel-tip needle in 3D environments with obstacles. Based on the Rapidly-exploring Random Trees (RRTs) method, we develop a motion planner to quickly build a tree to search the configuration space using a new exploring strategy, which generates new states using randomly sampled control space instead of the deterministically sampled one used in classic RRTs. Notice the fact that feasible paths might not be found for any given entry point and target configuration, we also address the feasible entry point planning problem to find feasible entry points in a specified entry zone for any given target configuration. To solve this problem, we developed a motion planning algorithm based on RRTs with backchaining, which grow backward from the target to explore the configuration space. Finally, simulation results with a approximated realistic prostate needle insertion environment demonstrate the performance of the proposed motion planner.