A criterion of evaluation of acoustic waveguide transformers (in the form of a bar, shell or plate) is worked out. The criterion allows to maximize a value of coefficient of transformation and to minimize a probability of failures because of endurance failures at the same time.
The criterion differs from known "quality factor", that was proposed by E.Eisner (Bell Telephone Lab., USA, New Jersey), so far as it needs no biparametric optimization of quality factor and coefficient of transformation separately as the criterion doesn't contain parameters that are associated with constants of the transformer material.
The results of criterion analysis of known classes of acoustic waveguide transformers are shown, for example of transformers with boundaries that can be described by elementary functions, by piece-continuous functions with discontinuity points of I kind, and by piece-smooth functions that are congruent in points of conjugation.
A new class of transformers is proposed. It has the best values of the criterion. Transformers of this class have profile's boundaries that are among the set of equilines of wave vector flow inside a canonical stepped waveguide transformer's profile and equilines are not the boundaries of the profile.