  We derive approximate analytical solutions to the environment-dependent
dilaton field theory equations in the presence of a one or two mirror system or
a sphere. The one-dimensional equations of motion are integrated for each
system. The solutions obtained herein can be applied to \textit{q}BOUNCE
experiments, neutron interferometry and for the calculation of the dilaton
field induced "Casimir force" in the \textsc{Cannex} experiment as well as for
Lunar Laser Ranging. They are typical of the Damour-Polyakov screening
mechanism whereby deviations from General Relativity are suppressed by a
vanishingly small direct coupling of the dilaton to matter in dense
environments.
