Monopiles are used as foundation structures for offshore wind energy towers, which are open-ended steel pipe piles with large diameters. For a pile foundation, the scour caused by wave and current lead to the reduction of embedded pile length and may decrease the lateral resistance. In the practical design different requirements regarding the minimum embedded pile length are used to limit the pile deflection at the mudline and at the pile toe under static and in particular cyclic loads due to wind and wave. The "vertical-tangent" and "zero-toe-kick" criteria are usually used to guarantee the lateral stability of monopiles and to insure piles are entered deep enough into the ground. In this study, the different design criteria are compared with respect to monopiles of scour. By means of the p-y curves method the pile deformation under lateral load are quantified and different criteria are assessed. The minimum required embedded lengths of monopile foundations with respect to scour are evaluated and the suitability of adopting the mentioned design criteria for monopile foundations is discussed.