  A {\em resolving set} for a graph $\Gamma$ is a collection of vertices $S$,
chosen so that for each vertex $v$, the list of distances from $v$ to the
members of $S$ uniquely specifies $v$. The {\em metric dimension} of $\Gamma$
is the smallest size of a resolving set for $\Gamma$.
  A graph is {\em distance-regular} if, for any two vertices $u,v$ at each
distance $i$, the number of neighbours of $v$ at each possible distance from
$u$ (i.e. $i-1$, $i$ or $i+1$) depends only on the distance $i$, and not on the
choice of vertices $u,v$. The class of distance-regular graphs includes all
distance-transitive graphs and all strongly regular graphs.
  In this paper, we present the results of computer calculations which have
found the metric dimension of all distance-regular graphs on up to 34 vertices,
low-valency distance transitive graphs on up to 100 vertices, strongly regular
graphs on up to 45 vertices, rank-$3$ strongly regular graphs on under 100
vertices, as well as certain other distance-regular graphs.
