The shape prediction of tendon-driven continuum manipulators is a challenging problem due to the effect of inner friction and external force. Many researchers use actuation displacement or actuation force as model input to predict the shapes of manipulators, but very few consider their relations and models able to predict the status of friction. This paper proposes a model-based method that combines the mechanics model with the kinematic model to predict the shapes of planar single-segment manipulators with consideration of external force and friction. Finally, the shape prediction of manipulators is converted to an optimization problem with actuation displacement and actuation force as the inputs of our algorithm. The distribution of tendon force and the situation of friction can be calculated by using the feedback data of the actuation unit even when actuation direction changes and hysteresis occurs. Experimental results indicate that the method has good performance in predicting the manipulator's shapes.