  Adopting Schwarzschild's orbit-superposition technique, we construct a series
of self-consistent galaxy models, embedded in the external field of galaxy
clusters in the framework of Milgrom's MOdified Newtonian Dynamics. These
models represent relatively massive ellipticals with a Hernquist radial profile
at various distances from the cluster centre. Using $N$-body simulations, we
perform a first analysis of these models and their evolution. We find that
self-gravitating axisymmetric density models, even under a weak external field,
lose their symmetry by instability and generally evolve to triaxial
configurations. A kinematic analysis suggests that the instability originates
from both box and non-classified orbits with low angular momentum. We also
consider a self-consistent isolated system which is then placed in a strong
external field and allowed to evolve freely. This model, just as the
corresponding equilibrium model in the same external field, eventually settles
to a triaxial equilibrium as well, but has a higher velocity radial anisotropy
and is rounder. The presence of an external field in MOND universe generically
predicts some lopsidedness of galaxy shapes.
