  Scalar field theories that possess a Vainshtein mechanism are able to
dynamically suppress the associated fifth forces in the presence of massive
sources through derivative non-linearities. The resulting equations of motion
for the scalar are highly non-linear and therefore very few analytic solutions
are known. Here we present a brief investigation of the structure of Vainshtein
screening in symmetrical configurations, focusing in particular on the
spherical, cylindrical and planar solutions that are relevant for observations
of the cosmic web. We consider Vainshtein screening in both the Galileon model,
where the non-linear terms involve second derivatives of the scalar, and a
k-essence theory, where the non-linear terms involve only first derivatives of
the scalar. We find that screening, and consequently the suppression of the
scalar force, is most efficient around spherical sources, weaker around
cylindrical sources and can be absent altogether around planar sources.
