We present a detailed analytical and numerical study of a novel type of sta
tic, superconducting, classically stable string texture in a renormalizable
topologically trivial massive U(1) gauge model with one charged and one ne
utral scalar. An upper bound on the mass of the charged scalar as well as o
n the current that the string can carry are established. A preliminary unsu
ccessful search for stable solutions corresponding to large superconducting
loops is also reported.