This paper considers robotic automation of a common surgical retraction primitive of exposing an underlying area by grasping and lifting a thin, 3D, possibly inhomogeneous layer of tissue. We present an algorithm that computes a set of stable and secure grasp-and-retract trajectories for a point-jaw gripper moving along a plane, and runs a 3D finite element (FEM) simulation to certify and assess the quality of each trajectory. To compute secure candidate grasp locations, we use a continuous spring model of thin, inhomogeneous deformable objects with linear energy potential. Experiments show that this method produces many of the same grasps as an exhaustive optimization with an FEM mesh, but is orders of magnitude cheaper: our method runs in O(v log v) time, where v is the number of veins, while the FEM computation takes O(pn3) time, where n is the number of nodes in the FEM mesh and p is the number of nodes on its perimeter. Furthermore, we present a constant tissue curvature (CTC) retraction trajectory that distributes strain uniformly around the medial axis of the tissue. 3D FEM simulations show that the CTC achieves retractions with lower tissue strain than circular and linear trajectories. Overall, our algorithm computes and certifies a high-quality retraction in about one minute on a PC. © 2009 IEEE.