The stability of a tape or film type high-critical-temperature superconductor of a large aspect ratio is studied by considering the transverse normal zone behavior across a cross-section subjected to an instantaneous and concentrated thermal disturbance. Different performance in terms of stable superconducting operation, current sharing, quenching, and superconductivity recovery have been identified. A stability criterion was developed based on heat conduction analyses for the current sharing steady state and the quenching steady state. The criterion was validated by the transient stability behavior results for a YBa2Cu3O7−x superconductor obtained through finite difference method. The effect of disturbance energy on the stability performance was also investigated.