A robotic system for flexible needle steering under ultrasound imaging. A robot is used to steer the needle along a predetermined curved trajectory by maneuvering the needle base. The needle tip position is detected by an ultrasound sensor and the tracking error of the needle tip from a predetermined needle path is input to a controller which solves the inverse kinematic based on the needle position, and the needle and tissue properties. The control algorithm uses a novel method to detect the elastic properties of the tissue by analyzing tissue motion at the region in front of the needle tip. The inverse kinematic solution may be performed on a model of the needle as a flexible beam having laterally connected virtual springs to simulate lateral forces exerted by the tissue elasticity. The system is able to direct the needle to a target within the tissue while circumventing forbidden regions.