  We find solutions of Einstein's field equation for topologically stable
strings associated with the breaking of a U(1) symmetry. Strings form in many
GUTs and are expected whenever the homotopy group $\Pi_1(M_0)$ is non-trivial.
The behavior of the fields making up the string is described by the
Euler-Lagrange equations. These fields appear in the energy-momentum tensor so
we must solve simultaneously for the coupled Einstein-scalar-gauge field
equations. Numerical results are obtained using a Taylor-series method. We
obtain a 5-parameter family of solutions and discuss their physical
characteristics. Significant gravitational lensing can occur due to strings
based on this model and are shown for different solutions. Finally, we prove
that the assumption of regularity at the string axis is not necessary by
looking at the physical properties of the string solutions.
