Panoramic line-scan cameras provide high definition images with a quasi uniform distribution of the sensing elements. Unfortunately, calibration of such devices with classic techniques is not possible making their use, in computer vision field, not straightforward. We propose a flexible and convenient calibration method for the computation of intrinsic and mechanism parameters of such systems by using images of a simple calibration pattern. Unlike existing approaches, the proposed method considers a full geometrical model and does not make any unattainable assumption such as concentricity of images, a priori knowledges about camera poses or coincidence of the rotation axis with the optical center. Using few images taken with free poses, the calibration is performed in two steps. First, the intrinsic parameters are computed using sets of 2D/3D point correspondences that are generated automatically by exploiting the structure of the calibration rig. Then, thanks to the parameterization of the projection of a 3D straight line, the mechanical parameters are computed using points at infinity. For each step, closed form solutions and iterative refinement techniques are presented. The proposed approach is validated with both synthetic and real data collected by our prototype.