The paper studies the physical mechanism of excitation of electromagnetic pulses (EMP) in terms of the phenomena of transition radiation of pulse high-current relativistic electron beam (HREP). The different schemes of beam radiator of EMR are considered. The mathematical solutions of problems are based on reducing of the initial electrodynamics problem to a system of boundary Hilbert problems. The considered schemes of EMR generation in term of transition radiation of HREP were highly efficient. The efficiency of EMR beam radiation for HREP parameters, which are easily realizable in experiment, can be 30–60 %.