In a solid oxide electrolysis cell (SOEC), the flow channel design influences the gas distribution, mass transfer, temperature distribution, and electrochemical properties significantly. This study evaluates the overall performance of SOECs with rectangular, triangular, trapezoidal, and semicircular flow channels and examines the effect of the geometry of the flow channel cross-section on the electrolysis process, gas flow, and material distribution. The trapezoidal flow channel shows the best electrochemical performance, but requires a high power and high pressure drop; the triangular flow channel has the most uniform gas velocity and distribution; and the semicircular flow channel shows the maximum gas velocity. The trapezoidal shape is found to be the optimal shape. Sensitivity analysis of the SOEC with the trapezoidal flow channel indicates that increasing the operating temperature improves the electrochemical performance, and reducing the inlet gas's steam volume fraction increases the gas conversion rate and decreases the electrolysis voltage.