In this paper we study the distance Ramsey number R D (s, t, d). The distance Ramsey number R 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 R d or G contains an induced t-vertex subgraph isomorphic to the distance graph in R d . We obtain the upper and lower bounds on R D (s, s, d), which are similar to the bounds for the classical Ramsey number R .