The magnetization curves, MJ(H), of long Josephson junction are computed from the dc Josephson equation with gauge-invariant phase. They are found to be reversible if α≡ L λJ<4, where L and λj are the junction length and the Josephson penetration depth, respectively. Irreversibility starts from α=4, and when α≫4, the MJ(H) curve is similar to that of type-II superconductors with a surface barrier. The corresponding fields for first vortex entry and last vortex exit are H1J=2JmaxλJ, where Jmax is the maximum local written current density, and H2J, which has a small positive value. © 1993.