The magnetic-field dependence of the critical current density in simpl
y connected Josephson medium (as an element of multiply connected supe
rconducting ceramics) has been considered semiphenomenologically. The
results are used to analyse the properties of the transport of current
in granular superconductors of finite dimensions. It has been shown t
hat the field dependence of the critical current density J(c)(H) alpha
(1 - H/H-0). This is in correspondence with the available experimental
results. The dependence of the critical current density on contact di
mensions of the weakly coupled grains is discussed.