A system of vortices formed near the boundary of a long periodically modulated Josephson contact has been calculated with account of the pinning due to inhomogeneity of the medium for the case of a monotonically growing external magnetic field at different values of the pinning parameter g which is proportional to the critical current and the spatial modulation period. It is shown that there exists a critical pinning parameter demarcating two regimes with different types of critical state. The obtained value differs from the value 0.9716 suggested by other researchers. The slope of the magnetic field profile near the boundary is obtained as a function of g.