Parametric deformable models are an important technique for image segmentation. In order to improve the robustness of the model, it may be interesting to incorporate a priori information about the shape of the objects to be segmented. In this paper, we propose to add a parallelism constraint. Such a model is relevant in many applications where elongated structures have to be detected. One main advantage of our formulation is that it only needs few parameters to be adjusted in addition to those of traditional snakes. The proposed model has been applied for the segmentation of OCT images of the retina and for the segmentation of retinal vessels. Experimental results, obtained on 25 OCT images and 30 eye fundus images, demonstrated the robustness, flexibility and large potential applicability of this new formulation. The accuracy of the method has been assessed by comparing manual segmentations, made by experts, with the automatic ones.