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The theoretical investigation of stationary vortex ring in an ideal incompressible fluid is carried out in this paper. Fraenkel’s procedure is used to obtain the stationary solution for vortex ring with uniform vorticity distribution. Further, based on finding solution Fraenkel’s procedure is modified to receive stationary vortex ring with isochronous vorticity distribution. The solutions of the uniform and isochronous problems are obtained in the form of an asymptotic expansion in the small parameter which characterised the ratio of the core and ring diameters. This work was supported by the Russian Science Foundation (project №17-11-01271).