In this talk, we investigate the local $p$-ranks of coverings of stable curves. Let $f : Y \to X$ be a morphism of stable curves over a complete discrete valuation ring with algebraically closed residue field of characteristic $p > 0$, $x$ a singular point of the special fiber $X_{s}$ of $X$. Suppose that the generic fiber $X_{\eta}$ of $X$ is smooth, and the morphism of generic fiber $f_{\eta}$ is a Galois etale covering with Galois group $G$. Write $Y'$ for the normalization of $X$ in the function field of $Y$, $g : Y' → X$ for the resulting normalization morphism, and $y'$ for a point of the inverse image of $x$ under the morphism $g$. Suppose that the inertia group $I_{y'}$ of $y'$ is an abelian $p$-group. Then we give an explicit formula for the $p$-rank of a connected component of $f^{-1}(x)$. Furthermore, we prove that the $p$-rank is bounded by $|I_{y'}|-1$.