Extending a model we previously used to calculate magnetization hysteresis arising from the geometrical barrier in a flat, bulk-pinning-free type-II superconducting strip subjected to a perpendicular magnetic field H a , we here calculate the contribution, arising from screening currents on the top and bottom surfaces, to the magnetic-field-dependent critical current I c (H a ) due to surface barriers, including both the geometrical barrier and the Bean-Livingston barrier. ͓S0163-1829͑98͒04946-7͔