Recently, continuum manipulators have drawn a lot of interest and effort from the robotic community, nevertheless control and modeling of such manipulators are still a challenging task especially because they require a continuum approach. In this paper, a general mechanical model with a geometrically exact approach for tendon-driven continuum manipulators is presented. This model can be applied to a wide range of manipulators thanks to the generality of the parameters which can be set. The approach proposed could as well be a powerful tool for developing the control strategy. The model is also capable of properly simulating the couple tendon drive, because it takes into account the torsion of the robot arm rather than neglecting it, as it is common practice in other existing models.