We present an algorithm for path planning for a flexible robot in complex environments. Our algorithm computes a collision free path by taking into account geometric and physical constraints, including obstacle avoidance, non-penetration, volume preservation, surface tension, and energy minimization. We describe a new algorithm for collision detection between a deformable robot and fixed obstacles using graphics processors. We also present techniques to efficiently handle complex deformable models composed of tens of thousands of polygons and obtain significant performance improvements over previous approaches. Moreover, we demonstrate a practical application of our algorithm in performing path planning of catheters in liver chemoembolization.