Abstract:The difficulties that exist in classical electromagnetic field theory are discussed and it is pointed out that the Maxwell s equation set in classical theory is not self-consistent and only the approximate solutions can be gotten in classical electromagnetic theory. And how to establish the modern electromagnetic field theory based on modern mathematics and concepts of modern physics is given for solving this problem. By the modern electromagnetic theory, the mathematical form for macroscopic electromagnetic field theory is obtained and the exact solutions for electromagnetic field boundary value problem can be gotten.