A tree representation distance method, applied to any dissimilarity array, always gives a valued tree, even if the tree model is not appropriate. In the first part, we propose some criteria to evaluate the quality of the computed tree. Some of them are metric; their values depend on the edge’s lengths. The other ones only depend on the tree topology. In the second part, we calculate the average and the critical values of these criteria, according to parameters. Three models of distance are tested using simulations. On the one hand, the tree model, and on the other hand, euclidean distances, and boolean distances. In each case, we select at random distances fitting these models and add some noise. We show that the criteria values permit one to differentiate the tree model from the others. Finally, we analyze a distance between proteins and its tree representation that is valid according to the criteria values.