<p><b>Abstract</b>—The shear-sort algorithm [<ref rid="bibt113219" type="bib">19</ref>] on an SIMD mesh model requires <tmath>$4\sqrt N+o\left( {\sqrt N} \right)$</tmath> time for sorting <it>N</it> elements arranged on a <tmath>$\sqrt N\times \sqrt N$</tmath> mesh. In this paper, we present an algorithm for sorting <it>N</it> elements in time <it>O</it>(<it>N</it><super>1/4</super>) on an SIMD Multi-Mesh architecture, thereby significantly improving the order of the time complexity. The Multi-Mesh architecture [<ref rid="bibt113223" type="bib">23</ref>], [<ref rid="bibt113224" type="bib">24</ref>] is built around <it>n</it><super>2</super> blocks, where each block is an <it>n</it>×<it>n</it> mesh with <it>n</it> = <it>N</it><super>1/4</super>, so that each processor will uniformly have four neighbors in the final topology.</p>