  We performed first - principles relativistic full-potential linearized
augmented plane wave calculations for strained tetragonal ferromagnetic
La(Ba)MnO$_3$ with an assumed experimental structure of thin strained
tetragonal La$_{0.67}$Ca$_{0.33}$MnO$_3$ (LCMO) films grown on SrTiO$_3$[001]
and LaAlO$_3$[001] substrates. The calculated uniaxial magnetic anisotropy
energy (MAE) values, are in good quantitative agreement with experiment for
LCMO films on SrTiO$_3$ substrate. We also analyze the applicability of linear
magnetoelastic theory for describing the stain dependence of MAE, and estimate
magnetostriction coefficient $\lambda_{001}$.
