  We study the depinning transitions of elastic strings in disordered media in
two different cases. We consider the elastic forces to be of infinite range in
one case, where the magnitude is proportional to the extension of the string.
The critical points and elastic behavior can be estimated to some extent in
this case. The exponents are estimated numerically and scaling relations are
found to be obeyed. We have also considered a model where the elastic force is
constant in magnitude. The critical points can again be argued and the critical
exponents are numerically estimated. The scaling relations are well obeyed.
Both of these models do not fall into known universality classes.
