  A family of exact vacuum solutions, representing generalized plane waves
propagating on the (anti-)de Sitter background, is constructed in the framework
of Poincar\'e gauge theory. The wave dynamics is defined by the general
Lagrangian that includes all parity even and parity odd invariants up to the
second order in the gauge field strength. The structure of the solution shows
that the wave metric significantly depends on the spacetime torsion.
