Аннотация:At this work we consider computer simulation results using 2 approaches to the problem of diffraction on slowing axially symmetric periodic structure. The first one evolves the construction of a source function (Green function) as a realisation of rigorous solution of a diffraction problem. Reduces to Fregholm integral equation of second kind and than numerical solving of using conjugate operator formalism (later referred as integral equation method). The second one is based on eigenmodes of axially symmetric periodic structures called a matrix multimode method. It considers Smith-Parcel radiation nearby the Wood`s anomaly as excitation of eigenmodes in axially symmetric periodic structures with certain boundary condition