  The recent starting of the gravitational wave (GW) astronomy with the events
GW150914, GW151226, GW170104, and the very recent GW170814 and GW170817 seems
to be fundamental not only in order to obtain new intriguing astrophysical
information from our surrounding Universe, but also in order to discriminate
among Einstein's general theory of relativity (GTR) and alternative
gravitational theories. At the present time, despite the cited events, and in
particular the last ones, which are the events GW170814 and GW170817, have put
very strong constraint on the GTR, extended theories of gravity have not been
completely ruled out. Here we discuss, in our knowledge for the first time in
the literature, GWs in the Rastall theory of gravity. In fact, the Rastall
theory recently obtained a renovated interest in the literature. We show that
there is a profound analogy between GWs in f(R) theories of gravity and GWs in
the Rastall theory. This will permit us to linearize the Rastall field
equations and to find the corresponding GWs. We will also study the motion of
the test masses due to GWs in this theory which could help, in principle, to
discriminate between the GTR, f(R) theories and the Rastall theory of gravity.
