  We consider gravitational collapse for the axially symmetric Einstein-Vlasov
system. We investigate the weak cosmic censorship conjecture in the case of
highly prolate initial data and we investigate the ``only if" part of the Hoop
conjecture. Shapiro and Teukolsky initiated a similar study in 1991
\cite{Shapiro1991} where they found support that the weak cosmic censorship
conjecture was violated for sufficiently prolate spheroidal initial data. More
recently, independent studies of this problem have been carried out by Yoo,
Harada and Okawa \cite{Yoo2017} and by East \cite{East2019}. A common feature
in these works is that the initial data are dust-like. Dust can be considered
as a \textit{singular} case of matter described by the Einstein-Vlasov system.
The original motivation by Shapiro and Teukolsky to study this problem is based
on the Lin-Mestel-Shu instability for gravitational collapse of uniform
spheroids in the case of dust in Newtonian gravity. We argue that the
Lin-Mestel-Shu solution is not relevant for studying the weak cosmic censorship
of the Einstein-Vlasov system and we argue that dust-like initial data is also
not relevant. To investigate collapse of highly prolate spheroidal
configurations for the Einstein-Vlasov system is nevertheless interesting in
view of the Hoop conjecture. By choosing highly prolate initial data the weak
cosmic censorship conjecture is seriously tested. We carry out such a study for
initial data which are not dust-like. We find formation of an apparent horizon
in all cases we consider, which provides support for the weak cosmic censorship
conjecture. In our tests of the Hoop conjecture we compute the polar
circumference $\mathcal{C}_{H,p}$ at the time when the apparent horizon forms
and find that it is less than 12% above $4\pi M$, where $M$ is the irreducible
mass of the apparent horizon, which agrees with the spirit of the Hoop
conjecture.
