  We explore the constraints imposed by the cancellation of triangle anomalies
on models in which the flavour anomalies reported by LHCb and other experiments
are due to an extra U(1)' gauge boson Z'. We assume universal and rational
U(1)' charges for the first two generations of left-handed quarks and of
right-handed up-type quarks but allow different charges for their
third-generation counterparts. If the right-handed charges vanish, cancellation
of the triangle anomalies requires all the quark U(1)' charges to vanish, if
there are either no exotic fermions or there is only one Standard Model singlet
dark matter (DM) fermion. There are non-trivial anomaly-free models with more
than one such `dark' fermion, or with a single DM fermion if right-handed
up-type quarks have non-zero U(1)' charges. In some of the latter models the
U(1)' couplings of the first- and second-generation quarks all vanish,
weakening the LHC Z' constraint, and in some other models the DM particle has
purely axial couplings, weakening the direct DM scattering constraint. We also
consider models in which anomalies are cancelled via extra vector-like leptons,
showing how the prospective LHC Z' constraint may be weakened because the
$Z^\prime \to \mu^+ \mu^-$ branching ratio is suppressed relative to other
decay modes.
