The isothermal remanent magnetization Mrem of an YBa2Cu3O7 crystal was measured as function of the maximum applied field 10 Oe≤Hm ≤40 kOe, for several isotherms 4.2K≤ T≤65K, for Hm⊥c and Hm∥c. Above an onset field for flux penetration Hp, Mrem initially increases sharply with Hm and then crosses over to a saturation value. An extended Bean model is used to fit the Mrem(H) data. The derived onset field for T>50K is approximately linear with T and is in agreement with the lower critical fields Hc1(T) measured by other techniques. At lower temperatures, however, Hp continues to increase. We incorporate surface barriers in the extended Bean model and consider the possibility that the low-temperature increase in Hp might be due to such barriers. © 1990.