  Thickness dependence and strain effects in films of $La_{1-x}A_xMnO_3$
perovskites are analyzed in the colossal magnetoresistance regime. The
calculations are based on a generalization of a variational approach previously
proposed for the study of manganite bulk. It is found that a reduction in the
thickness of the film causes a decrease of critical temperature and
magnetization, and an increase of resistivity at low temperatures. The strain
is introduced through the modifications of in-plane and out-of-plane electron
hopping amplitudes due to substrate-induced distortions of the film unit cell.
The strain effects on the transition temperature and transport properties are
in good agreement with experimental data only if the dependence of the hopping
matrix elements on the $Mn-O-Mn$ bond angle is properly taken into account.
Finally variations of the electron-phonon coupling linked to the presence of
strain turn out important in influencing the balance of coexisting phases in
the film
