  The global properties of static perfect-fluid cylinders and their external
Levi-Civita fields are studied both analytically and numerically. The existence
and uniqueness of global solutions is demonstrated for a fairly general
equation of state of the fluid. In the case of a fluid admitting a
non-vanishing density for zero pressure, it is shown that the cylinder's radius
has to be finite. For incompressible fluid, the field equations are solved
analytically for nearly Newtonian cylinders and numerically in fully
relativistic situations. Various physical quantities such as proper and
circumferential radii, external conicity parameter and masses per unit
proper/coordinate length are exhibited graphically.
