let $z$ be a variety and $a$ an elliptic curve over the function field of $z$. i. dolgachev and m. gross define the \emph{geometric shafarevich-tate group} of $a$ over $z$ to classify the set of isomorphism classes of principal homogeneous spaces for $a$ which are locally trivial in the \'etale topology. in joint work with chad schoen, we describe how to compute the shafarevich-tate group when $a$ is the generic fiber of a class of elliptic threefolds and $z$ is the base. we also obtain results on the brauer groups of such threefolds.