A Central Solenoid (CS) conductor layout has been tentatively decided during the conceptual design phase of the Chinese Fusion Engineering Testing Reactor (CFETR). To check the validity of the conductor layout, stability analysis must be performed against the working condition of the conductors. We constructed a superconducting critical surface of the strands used in the CS conductors and then calculated the current sharing temperature of the conductors under the most stringent working condition envisioned with the operation parameters. We further analyzed the energy margin by simulating the quenching behavior with the GANDALF code upon disturbances of different durations and lengths representative of a mechanical disturbance and plasma disruption. The analysis results give preliminary estimation of conductor stability for further improvement of the design.