  Let $G$ be a nontrivial connected and edge-colored graph. An edge-cut $R$ of
$G$ is called a rainbow cut if no two edges of it are colored with a same
color. An edge-colored graph $G$ is called rainbow disconnected if for every
two distinct vertices $u$ and $v$ of $G$, there exists a $u-v$ rainbow cut
separating them. For a connected graph $G$, the rainbow disconnection number of
$G$, denoted by $rd(G)$, is defined as the smallest number of colors that are
needed in order to make $G$ rainbow disconnected. In this paper, we will study
the Erd\H{o}s-Gallai-type results for $rd(G)$, and completely solve them.
