Two- and three-body Y-N potentials including the rescattering corrections are calculated by using Miyazawa's method. The Y-N systems are treated by the two-channel formalism in the case of T=1/2: The one is the channel of the Σ-N system and the other is of the Λ-N system. Then the potential is defined as the 2 ×2 matrix form. The three-body force vanishes, in which no direct two-nucleon interaction is considered, if the π-Λ rescattering corrections are not taken into account. The other type of the three-body force in which one pion is exchanged between each pair of the particles is also investigated.