A class of efficient methods for the numerical solution of the problem of Optimal Experimental Design is developed and tested on typical examples for D— and A—optimal design. Equivalence theorems are derived by Kuhn-Tucker conditions and the feasible directions approach of Nonlinear Programming. A method for construction of the initial approximation in the case of D—optimal design is proposed and tested. The method yields the exact solution in many cases. Newton’s methods are tested in the D—optimal design case.