  We investigate the existence of inhomogeneous exact solutions in Weyl
Integrable theory with a matter source. In particular, we consider the
existence of a dust fluid source while for the underlying geometry we assume a
line element which belongs to the family of silent universes. We solve
explicitly the field equations and we find the Szekeres spacetimes in Weyl
Integrable theory. We show that only the isotropic family can describe
inhomogeneous solutions where the LTB spacetimes are included. A detailed
analysis of the dynamics of the field equations is given where the past and
future attractors are determined. It is interesting that the Kasner spacetimes
can be seen as past attractors for the gravitation models, while the unique
future attractor describes the Milne universe similar with the behaviour of the
gravitational model in the case of General Relativity.
