The medical endoscope consists in a rigid tube with optical elements inside that transfer the projection center of the objective lens at one end, to a virtual point at the other end. The endoscope is a non-conventional camera that presents severe non-linear distortions. Moreover it does not necessarily follow perspective projection, specially when mechanical torsion is applied to the probe. In order to study these aspects we describe a ray-based calibration procedure, with no prior assumptions about centrality or specific distortion models. The accuracy of the achieved calibration is slightly more than one tenth of millimeter. In addition, we quantify the errors in approximating the projection by a central model, and test the accuracy of the Bouguet's toolbox in calibrating this specific system.