  The static stress needed to depin a 2D edge dislocation, the lower dynamic
stress needed to keep it moving, its velocity and displacement vector profile
are calculated from first principles. We use a simplified discrete model whose
far field distortion tensor decays algebraically with distance as in the usual
elasticity. An analytical description of dislocation depinning in the strongly
overdamped case (including the effect of fluctuations) is also given. A set of
$N$ parallel edge dislocations whose centers are far from each other can depin
a given one provided $N=O(L)$, where $L$ is the average inter-dislocation
distance divided by the Burgers vector of a single dislocation. Then a limiting
dislocation density can be defined and calculated in simple cases.
