Thermodynamic cycle analysis is presented to estimate the maximum liquefaction rate of hydrogen for various systems using a Gifford-McMahon(GM) cryocooler. Since the present authors` previous experiments showed that the gaseous hydrogen was liquefied approximately at the rate of 5.1 mg/s from the direct contact with a commercial two-stage GM refrigerator, this study has been proposed to predict how much the liquefaction rate can be increased in different configurations using the GM cooler and with improved heat exchangers. The optimal operating conditions have been analytically sought with real properties of normal hydrogen for the Linde-Hampson(L-H) system precooled by single-stage GM, the direct-contact system with two-stage GM, the L-H system precooled by two-stage GM, and the direct-contact system with helium GM-JT (Joule-Thomson). The maximum liquefaction rate has been predicted to be only about 7 times greater than the previous experiment, even though the highly effective heat exchangers may be employed. It is concluded that the liquefaction rate is limited mainly because of the cooling capacity of the commercially available GM cryocoolers and a practical scale of hydrogen liquefaction is possible only if the GM cooler has a greater capacity at 70-100 K.