  A double new class of solutions to the general relativity field equations
describing interior spacetimes sourced by stationary cylindrical anisotropic
fluids with principal stress directed along the symmetry axis is displayed.
These solutions are required to satisfy regularity and junction conditions so
that they can be possibly used to represent rotating astrophysical objects.
Mathematical and physical properties are analyzed. The spacetime two
independent parameters are physically interpreted, and they are shown to define
two different solution classes together with stating the latters' properties.
