  Given a positive function $F$ on $S^n$ which satisfies a convexity condition,
for $1\leq r\leq n$, we define the $r$-th anisotropic mean curvature function
$H^F_r$ for hypersurfaces in $\mathbb{R}^{n+1}$ which is a generalization of
the usual $r$-th mean curvature function. We prove that a compact embedded
hypersurface without boundary in $\R^{n+1}$ with $H^F_r={constant}$ is the
Wulff shape, up to translations and homotheties. In case $r=1$, our result is
the anisotropic version of Alexandrov Theorem, which gives an affirmative
answer to an open problem of F. Morgan.
