Abstract-Medical procedures such as seed implantation, biopsies, and treatment injections require inserting a needle to a specific target location inside the human body. Flexible needles with bevel tips are known to bend when inserted into soft tissues and can be inserted to targets unreachable by rigid symmetric-tip needles. Planning for such procedures is difficult because needle insertion causes soft tissues to displace and deform. In this paper, we develop a 2D planning algorithm for insertion of highly flexible bevel-tip needles into tissues with obstacles. Given an initial needle insertion plan specifying location, orientation, bevel rotation, and insertion distance, the planner combines soft tissue modeling and numerical optimization to generate a needle insertion plan that compensates for simulated tissue deformations, locally avoids polygonal obstacles, and minimizes needle insertion distance. Soft tissue deformations are simulated using a finite element formulation that models the effects of needle tip and frictional forces using a 2D mesh. The planning problem is formulated as a constrained nonlinear optimization problem which is locally minimized using a penalty method that converts the formulation to a sequence of unconstrained optimization problems. We apply the planner to bevel-right and bevel-left needles and generate plans for targets that are unreachable by rigid needles.