  Let $G$ be a digraph and $r(G)$ be its rank. Many interesting results on the
rank of an undirected graph appear in the literature, but not much information
about the rank of a digraph is available. In this article, we study the rank of
a digraph using the ranks of its blocks. In particular, we define classes of
digraphs, namely $r_2$-digraph, and $r_0$-digraph, for which the rank can be
exactly determined in terms of the ranks of subdigraphs of the blocks.
Furthermore, the rank of directed trees, simple biblock graphs, and some simple
block graphs are studied.
