The linearized suffix tree (LST) is an array data structure supporting traversals on suffix trees. We apply this LST to two dimensional (2D) suffix trees and obtain a space-efficient substitution of 2D suffix trees. Given an $n{ imes}n$ text matrix and an $m{ imes}m$ pattern matrix over an alphabet ${Sigma}$, our 2D-LST provides pattern matching in $O(m^2log{mid}{Sigma}{mid})$ time and $O(n^2)$ space.