Effects of stretch on the pulsating instability of rich hydrogen/air premixed flames, which are characterized by large Lewis numbers, were analytically and computationally investigated via the negatively stretched inwardly propagating spherical flame (IPF) and the positively stretched counterflow flame (CFF). Analytical results yield explicit criteria for the onset of pulsation, and show that positive stretch promotes pulsation while negative stretch retards it. Computational results for the IPF show that the flame initially propagates at the laminar flame speed when the flame radius is large. Oscillation subsequently develops, and is then amplified, damped, and eventually suppressed when the flame is still sufficiently far away from the center. Thus negative stretch tends to suppress the occurrence of pulsating instability, and thereby extend the flammable range of rich hydrogen/air flames beyond that of their unstretched, planar counterpart. Furthermore, the pulsating propagation is quasi-steady in that it is independent of the initial state. Computational results for the CFF show that oscillation is initiated at an equivalence ratio much smaller than the one-dimensional rich threshold, and that the critical strain rate leading to pulsation is smaller than the corresponding static extinction limit. Furthermore, similar to the one-dimensional, unstretched cases, with progressive increase in the strain rate for a sufficiently rich mixture, the pulsation mode changes from that of monochromatic, to period doubling, and to permanent extinction. The pulsating flames are also quasi-steady in nature in that the period of oscillation is larger than the characteristic flame time. As such, the unsteady flame cannot recover once the instantaneous flame temperature is reduced below the corresponding steady-state extinction temperature, Because pulsating extinction occurs at a smaller strain rate than the steady extinction limit, the flame extinguishes in the pulsating instead of the steadily propagating mode, and the flammable range is accordingly narrowed. Finally, the numerically calculated critical states at which the IPF and the CFF respectively lose stability are predicted well by using the analytically derived transition criteria and global flame parameters.