Minimally invasive medical procedures such as biopsies, anesthesia drug injections, and brachytherapy cancer treatments require inserting a needle to a specific target inside soft tissues. This is difficult because needle insertion displaces and deforms the surrounding soft tissues causing the target to move during the procedure. To facilitate physician training and preoperative planning for these procedures, we develop a needle insertion motion planning system based on an interactive simulation of needle insertion in deformable tissues and numerical optimization to reduce placement error. We describe a 2-D physically based, dynamic simulation of needle insertion that uses a finite-element model of deformable soft tissues and models needle cutting and frictional forces along the needle shaft. The simulation offers guarantees on simulation stability for mesh modifications and achieves interactive, real-time performance on a standard PC. Using texture mapping, the simulation provides visualization comparable to ultrasound images that the physician would see during the procedure. We use the simulation as a component of a sensorless planning algorithm that uses numerical optimization to compute needle insertion offsets that compensate for tissue deformations. We apply the method to radioactive seed implantation during permanent seed prostate brachytherapy to minimize seed placement error.