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A simple model for the formation of a straight cosmic string, wiggly or unperturbed is considered. The gravitational field of such string is computed in the linear approximation. The vacuum expectation value of the stress tensor of a massless scalar quantum field coupled to the string gravitational field is computed to the one loop order. Finally, the back-reaction effect on the gravitational field of the string is obtained by solving perturbatively the semiclassical Einstein's equations.doi:10.1103/physrevd.52.4319 pmid:10019659 fatcat:l4uxo7ib7fhcpchwz4joz5j4s4