  There are some gravitational theories in which the ordinary energy-momentum
conservation law is not valid in the curved spacetime. Rastall gravity is one
of the known theories in this regard which includes a non-minimal coupling
between geometry and matter fields. Equipped with the basis of such theory, we
study the properties of traversable wormholes with flat asymptotes. We
investigate the possibility of exact solutions by a source with the baryonic
matter state parameter. Our survey indicates that Rastall theory has
considerable effects on the wormhole characteristics. In addition, we study
various case studies and show that the weak energy condition may be met for
some solutions. We also give a discussion regarding to traversability of such
wormhole geometry with phantom sources.
