A set of vertices

resolves a graph

if every vertex is uniquely
determined by its vector of distances to the vertices in

. A metric
dimension of

is the minimum cardinality of a resolving set of

. A
bipartite graph

is a graph whose vertex set

can be partitioned
into two subsets

and

with

such that every edge
of

joins

and

. The graph

is called

-regular if every
vertex of

is adjacent to

other vertices. In this paper, we
determine the metric dimension of

-regular bipartite graphs

where

or

.