Shearing mechanisms of the primary strengthening phase in cobalt-base and cobalt-nickel-base superalloys, γ′ (L12), are investigated at the elementary defect level by using a combination of generalized-stacking-fault energy (GSF) calculations and phase field simulations. The GSF energy surfaces of the γ and γ′ phases, as determined from available experimental data and ab initio calculations, are used in the phase field simulations. Sophisticated deformation pathways leading to various planar defects including antiphase boundaries (APB), remnant superlattice intrinsic stacking faults (SISF), APB-SISF-APB ribbons and SISF islands are predicted as a function of alloy composition and particle shapes. The predicted stacking fault configurations for both alloys are consistent with recent transmission electron microscopy observations. Effects of dislocation line tension difference in γ and γ′ phases and planar defect energy variation due to segregation at the planar defects are discussed. The detailed dislocation core structures, effects of dislocation line tension differences on deformation mechanisms, and unique deformation mechanisms uncovered, which include stacking fault ribbon shearing, antiphase boundary shearing, and mixed modes, could be used to improve constitutive microstructure-property relationships in advanced crystal plasticity modeling and to assist in alloy design.