Giant electromechanical coupling factor of k31 mode over 86% was found for (100) Pb[(Zn1/3Nb2/3)0.91Ti0.09]O3 and (110) Pb[(Mg1/3Nb2/3)0.74Ti0.26]O3 single-crystal plates poled in the  and  directions, respectively. The P-E hysteresis loops in the single-crystal plates with giant k31 became asymmetric. Furthermore, the frequency response of impedance in these plates with giant k31 consisted of a single vibration in the length direction. A mechanism to realize giant k31 can be explained by the relationship between the crystal plane and poling direction. In addition, the existence of giant piezoelectric d31 constant was proven by the strain measurement as well as by the impedance measurement.