The work is devoted to analysis of Atomic Functions (AF) applications to principal problems of antennas theory. The analysis follows the result of the solution of some applied problems, such as is to deter-mine the field of antenna in the far zone when the distribution of the current or the tangential components of the electromagnetics field on the surface of antenna is known, and of synthesis is to determine a current (or a field) in the antenna by means of radiation pattern in the zone, and boundary value problems of the antenna theory is to determine the field in antenna and surrounding area when excitation by outside sources and boundary conditions are known. In the second part of paper, the new algorithm for numerical solution of radiation pattern synthesis problems is proposed. A number of numerical examples were performed to illustrate the effectiveness of presented approach. Unique approximating proper-ties of Atomic Functions (AF) let us apply more simple and effective method, which result in significant computational gain, and, hence, the solution requires less memory and run time.