  We study the mean-field version of a model proposed by Leschhorn to describe
the depinning transition of interfaces in random media. We show that evolution
equations for the distribution of forces felt by the interface sites can be
written down directly for an infinite system. For a flat distribution of random
local forces the value of the depinning threshold can be obtained exactly. In
the case of parallel dynamics (all unstable sites move simultaneously), due to
the discrete character of the allowed interface heights, the motion of the
center of mass is non-uniform in time in the moving phase close to the
threshold and the mean interface velocity vanishes with a square-root
singularity.
