Snake-like manipulators with a large, open lumen can offer improved treatment alternatives for minimally-and less-invasive surgeries. In these procedures, surgeons use the manipulator to introduce and control flexible tools in the surgical environment. This paper describes a predictive algorithm for estimating manipulator configuration given tip position for nonconstant curvature, cable-driven manipulators using energy minimization. During experimental bending of the manipulator with and without a tool inserted in its lumen, images were recorded from an overhead camera in conjunction with actuation cable tension and length. To investigate the accuracy, the estimated manipulator configuration from the model and the ground-truth configuration measured from the image were compared. Additional analysis focused on the response differences for the manipulator with and without a tool inserted through the lumen. Results indicate that the energy minimization model predicts manipulator configuration with an error of 0.24 ± 0.22mm without tools in the lumen and 0.24 ± 0.19mm with tools in the lumen (no significant difference, p = 0.81). Moreover, tools did not introduce noticeable perturbations in the manipulator trajectory; however, there was an increase in requisite force required to reach a configuration. These results support the use of the proposed estimation method for calculating the shape of the manipulator with an tool inserted in its lumen when an accuracy range of at least 1mm is required.