In previous work, we used a matched asymptotic technique to investigate the fields near an edge of a finitely conducting strip with nonzero thickness, It was demonstrated that with this asymptotic solution of the fields, the power loss in the region local to the edge could be determined accurately, In this paper, we will show how the accurate representation of the power loss can be used to obtain a dosed form expression for the attenuation constant due to;conductor loss of coplanar waveguide (CPW) structures, This expression is valid for an arbitrarily shaped edge and any conductor thickness, Results obtained with this expression are compared to and closely agree with both experimental results and other techniques found in the literature. We also investigated conductors with different edge shapes (45 degrees and 90 degrees edges) to explore their effect on the attenuation constant (or loss) of CPW structures.