  In this paper we study the distance Ramsey number $R_{{\it D}}(s,t,d)$. The
\textit{distance Ramsey number} $R_{{\it D}}(s,t,d) $ is the minimum number $n$
such that for any graph $ G $ on $ n $ vertices, either $G$ contains an induced
$ s $-vertex subgraph isomorphic to a distance graph in $ \Real^d $ or $ \bar
{G} $ contains an induced $ t $-vertex subgraph isomorphic to the distance
graph in $ \Real^d $. We obtain the upper and lower bounds on $R_{{\it
D}}(s,s,d),$ which are similar to the bounds for the classical Ramsey number
$R(\lceil \frac{s}{[d/2]} \rceil, \lceil \frac{s}{[d/2]} \rceil)$.
