  In this paper, we study the Steiner hyper-Wiener index of a graph, which is
obtained from the standard hyper-Wiener index by replacing the classical graph
distance with the Steiner distance. It is shown how this index is related to
the Steiner Hosoya polynomial, which generalizes similar result for the
standard hyper-Wiener index. Next, we show how the Steiner $3$-hyper-Wiener
index of a modular graph can be expressed by using the classical graph
distances. As the main result, a method for computing this index for median
graphs is developed. Our method makes computation of the Steiner
$3$-hyper-Wiener index much more efficient. Finally, the method is used to
obtain the closed formulas for the Steiner $3$-Wiener index and the Steiner
$3$-hyper-Wiener index of grid graphs.
