The [r,s,t]-coloring is a generalization of the classical vertex, edge, and total colorings, where two vertices, two edges, and a vertex and its incident edges have colors distant by at least r, s and t, respectively. The square of a graph G is a graph obtained from G by adding an edge between two vertices at a distance at most 2 in G. A cylindrical grid is equivalent to the Cartesian product of a path and a cycle. In this article, colorings for the square of cylindrical grids are discussed. It is shown that such graphs are class one graphs (according to Vizing’s theorem). For the [r,s,t]-coloring of these graphs, particular values of r, s and t are presented, for which the minimum number of colors needed in an [r,s,t]-coloring is determined.