The initial data of the gravitational field produced by a thick loop string are considered. We show that a thick loop is not a geodesic on the initial hypersurface, while a loop conical singularity is. This suggests that there is a critical thickness of a string, at which the linear perturbation theory with a flat space background fails to describe the gravity of a loop cosmic string. Using the above initial data, we also show that the linear perturbation around the flat space is plausible if the string thickness is larger than ∼5 × 10⁻³a, where a is the curvature radius of the loop.