  In the present paper, we give some sufficient conditions for
$\operatorname{Cl}(\Bbbk[P])$ to be torsionfree, where
$\operatorname{Cl}(\Bbbk[P])$ denote the divisor class group of the toric ring
$\Bbbk[P]$ of an integral polytope $P$. We prove that
$\operatorname{Cl}(\Bbbk[P])$ is torsionfree if $P$ is compressed, and
$\operatorname{Cl}(\Bbbk[P])$ is torsionfree if $P$ is a $(0,1)$-polytope which
has at most $\dim P+2$ facets. Moreover, we characterize the toric rings of
$(0,1)$-polytopes in the case $\operatorname{Cl}(\Bbbk[P])\cong \mathbb{Z}$.
