Аннотация:We explorer reconstruction procedures for modified gravity cosmological models. The considering reconstruction procedures are proposed to reconstruct the potentials in cosmological models non-minimally coupled scalar fields and get models with suitable behaviour of the Hubble parameter and exact solutions. Such a method is similar to the Hamilton–Jacobi method (also known as the superpotential method or the first-order formalism) that applied to cosmological models with minimally coupled scalar fields. We show that this method is suitable for construction of induced gravity model with polynomial potentials. We also show that there are different algorithms of such reconstruction procedure for models with non-minimally coupled scalar fields.