  We consider anisotropic fluids with directional pressures $p_i = w_i \rho$
($\rho$ is the density, $w_i = $const, $i = 1,2,3$) as sources of gravity in
stationary cylindrically symmetric space-times. We describe a general way of
obtaining exact solutions with such sources, where the main features are
splitting of the Ricci tensor into static and rotational parts and using the
harmonic radial coordinate. Depending on the values of $w_i$, it appears
possible to obtain general or special solutions to the Einstein equations, thus
recovering some known solutions and finding new ones. Three particular examples
of exact solutions are briefly described: with a stiff isotropic perfect fluid
($p = \rho$), with a distribution of cosmic strings of azimuthal direction
(i.e., forming circles around the $z$ axis), and with a stationary combination
of two opposite radiation flows along the $z$ axis.
