  Interval minors of bipartite graphs were recently introduced by Jacob Fox in
the study of Stanley-Wilf limits. We investigate the maximum number of edges in
$K_{r,s}$-interval minor free bipartite graphs. We determine exact values when
$r=2$ and describe the extremal graphs. For $r=3$, lower and upper bounds are
given and the structure of $K_{3,s}$-interval minor free graphs is studied.
