Electrodynamics properties of the fractal antenna, that formed by two coplanar flat thin conductive rings are investigated. The frequency dependences of the input impedance, standing wave coefficient, directivity were calculated and analyzed by computer modeling. A comparative analysis of the testing characteristics of the antenna with the same parameters of ring frame was done. The study determined that the wideband and the high value of directional properties are advantages of antenna. Different mobile communication systems are possible areas of application of the test antenna, based on the analysis of its electrodynamic parameters.