Algebraic geometry can be used to solve identifiability problems in design of experiments as modern computational algebra packages such as Maple or CoCoA can be used. The point is that we regard the design as a set of polynomial solutions. Then, the Gröbner base theory allows one to identify the whole set of estimable effects (main or interactions) of the factors of the design. In this paper we applied Gröbner base theory in certain two level factorial designs.