Apparatus and methods for stabilizing and/or positioning tissues or organs during surgical procedures. One feature of the positioners of the invention includes the use of one or more suction elements used to grip the organ or tissue. The main body of the suction element comprises body defining a polyhedral shaped chamber, an elliptical ring structure and a vacuum port. The invention further includes structures to support the suction element and hold the suction element and attached tissue in a fixed position including catheters, lockable flexible arms, and retractors.