We develop a new motion planning algorithm for a variant of a Dubins car with binary left/right steering and apply it to steerable needles, a new class of flexible bevel-tip medical needles that physicians can steer through soft tissue to reach clinical targets inaccessible to traditional stiff needles. Our method explicitly considers uncertainty in needle motion due to patient differences and the difficulty in predicting needle/tissue interaction. The planner computes optimal steering actions to maximize the probability that the needle will reach the desired target. Given a medical image with segmented obstacles and target, our method formulates the planning problem as a Markov Decision Process based on an efficient discretization of the state space, models motion uncertainty using probability distributions, and computes optimal steering actions using Dynamic Programming. This approach only requires parameters that can be directly extracted from images, allows fast computation of the optimal needle entry point, and enables intra-operative optimal steering of the needle using the pre-computed dynamic programming look-up table. We apply the method to generate motion plans for steerable needles to reach targets inaccessible to stiff needles, and we illustrate the importance of considering uncertainty during motion plan optimization.