The mixed state of thin narrow superconducting films with an edge barr
ier placed in a transverse magnetic field is considered. The boundarie
s of the region for the existence of metastable mixed states with an a
ssigned number of vortices N [H-min(N)less than or equal to H less tha
n or equal to H-max(N)] are found. The magnetic-field dependence of th
e critical field is found for the films. The transition from the Meiss
ner state to the static mixed state is discussed. (C) 1998 American In
stitute of Physics. [S1063-7834(98)00210-X].