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In this paper, we study vacuum static spaces with positive isotropiccurvature. We prove that if $(M^n, g, f)$, $n \ge 4$, is a compact vacuumstatic space with positive isotropic curvature, then up to finite cover, $M$ isisometric to a sphere ${\Bbb S}^n$ or the product of a circle ${\Bbb S}^1$ withan $(n-1)$-dimensional sphere ${\Bbb S}^{n-1}$.

Vacuum Static Spaces with Positive Isotropic Curvature