A rigorous electrodynamic approach is used to solve the problem of Huygens element radiation over the interface of media. Green's functions of stratified media are used. The proposed method makes it possible to calculate the electromagnetic field of antennas in the near zone in which the radiation field has not yet been formed. The integrals for the components of the field in the far zone are calculated by the method of the steepest descent to confirm the correctness of the analytical expressions obtained. The field in the near zone is calculated by numerical integration over the wave numbers on the complex plane. Graphs of the distribution of the electromagnetic field over the interface of media for different heights and frequencies are given. Calculations are performed for different types of the underlying surface. The proposed approach makes it possible to analyze the radiation of antennas whose field is modeled by elementary emitters in the form of electric and magnetic dipoles.