The magnetic-field dependence of the critical currentI c(H) is considered for a short Josephson junction with the critical current density j c alternating along the tunnel contact. Two model cases, periodic and randomly alternating j c , are treated in detail. Recent experimental data on I c(H) for grain-boundary Josephson junctions in YBa 2Cu 3O x are discussed. @S0163-1829~97!51614-6# Considerable progress has recently been reported in understanding properties of grain-boundary Josephson junctions in YBa 2 Cu 3 O x ~YBCO! films. 1,2 The boundaries were found to have facets with a variety of orientations, the fact which, in conjunction with the d-wave symmetry of the order parameter, led to the conclusion that the critical current density j c may differ both in value and the sign at different facets. 2 This is offered as the reason for the grain-boundary critical current I c being significantly suppressed relative to the bulk value. 2,3 The dependence of I c on the applied field H, one of the major junction properties relevant for applications, has also been studied. The observed patterns I c(H) are manifestly non-Fraunhofer and difficult for interpretation. 2‐5 We show in this paper that qualitative features of these patterns can be attributed to the basic fact that the local critical current density j c changes sign from one facet to another. Moreover, the alternating character of j c results in a shift of the major maximum in I c(H) from H50 of the standard Fraunhofer pattern to a position related to periodicity in the distribution of j c (x), where x is the axis along the tunnel contact. Random deviations from periodicity change dramatically patterns of I c(H). In the following we calculate the critical current I c for a Josephson junction with the length L!l J , a typical value of the local Josephson penetration depth. The current density across the junction is j (x)5 j c(x)sinw(x), where w(x) is the phase difference. The magnetic field H is nearly constant inside a short Josephson junction; in this case 6