Current configurations in a periodically modulated long Josephson contact located in an external magnetic field are considered for values of the pinning parameter I greater than and less than the critical one (Iс). It is shown that, if I > Iс, the maximum value of the non-quenching current is determined by the contact length and does not depend on the value of the external magnetic field. In the case I < Iс, the critical current is determined by the value of the magnetic field at which the vortices begin to fill the entire length of the contact, and does not depend on the length of the contact. At the same time, with the growth of the external magnetic field, the critical value of the current decreases.