Wormhole configurations in Einstein’s general theory of relativity (GR) require exotic matter sources violating the weak energy condition (WEC). Rastall’s theory is a generalization of GR in its matter source considering a nonconserved energy momentum (EM) tensor. Hence, on the one hand, the nature of this generalization of the matter source of field equations and, on the other hand, the possibility of respecting energy conditions for dynamical wormholes in contrast with static ones motivates us to study the possibility of existence of wormhole configurations respecting energy conditions or minimizing the violations of them in Rastall’s modified theory. We derive general analytical solutions considering a constant redshift functions and a particular equation of state for energy density and pressure profiles. We show that because of the modifications in EM source of the field equations, there exist solutions respecting the WEC in the vicinity of the wormhole’s throat for a specified values of the parameters. Some particular solutions are discussed in detail.