This paper proposes a robust deformable adaptive 2D model, based on computer vision methods, that automatically fits the body (ventral silhouette) of Bluefin tuna while swimming. Our model (without human intervention) adjusts to fish shape and size, obtaining fish orientation, bending to fit their flexion motion and has proved robust enough to overcome possible segmentation inaccuracies. Once the model has been successfully fitted to the fish it can ensure that the detected object is a tuna and not parts of fish or other objects. Automatic requirements of the fishing industry like biometric measurement, specimen counting or catch biomass estimation could then be addressed using a stereoscopic system and meaningful information extracted from our model. We also introduce a fitting procedure based on a fitting parameter-Fitting Error Index (FEI)-which permits us to know the quality of the results. In the experiments our model has achieved very high success rates (up to 90%) discriminating individuals in highly complex images acquired for us in real conditions in the Mediterranean Sea. Conclusions and future improvements to the proposed model are also discussed.