  Cylindrically symmetric static manifolds are classified according to their
homotheties and metrics. In each case the homothety vector fields and the
corresponding metrics are obtained explicitly by solving the homothety
equations. It turns out that these metrics admit homothety groups $H_m$, where
$m=4,5,7,11$. This classification is then used to identify the cylindrically
symmetric static spaces admitting the local homotheties, which are globally
prohibited due to their topological construction. Einstein's field equations
are then used to identify the physical nature of the spaces thus obtained.
