  We apply the method developed in Ref. [S.B.Chernyshuk and B.I.Lev,
Phys.Rev.E, \textbf{81}, 041701 (2010)] for theoretical investigation of
colloidal elastic interactions between axially symmetric particles in the
confined nematic liquid crystal (NLC) near one wall and in the nematic cell
with thickness $L$. Both cases of homeotropic and planar director orientations
are considered. Particularly dipole-dipole, dipole-quadrupole and
quadrupole-quadrupole interactions of the \textit{one} particle with the wall
and within the nematic cell are found as well as corresponding \textit{two
particle} elastic interactions. A set of new results has been predicted: the
effective power of repulsion between two dipole particles at height $h$ near
the homeotropic wall is reduced gradually from inverse 3 to 5 with an increase
of dimensionless distance $r/h$; near the planar wall - the effect of
dipole-dipole \textit{isotropic attraction} is predicted for large distances
$r>r_{dd}=4.76 h$; maps of attraction and repulsion zones are crucially changed
for all interactions near the planar wall and in the planar cell; one dipole
particle in the homeotropic nematic cell was found to be shifted by the
distance $\delta_{eq}$ from the center of the cell \textit{independent} of the
thickness $L$ of the cell. The proposed theory fits very well with experimental
data for the confinement effect of elastic interaction between spheres in the
homeotropic cell taken from [M.Vilfan et al. Phys.Rev.Lett. {\bf 101}, 237801,
(2008)] in the range $1\div1000 kT$.
