Abstract: Let ${\cal R}=\Z[A^{\pm 1}, \delta^{-1}]$, where $\delta=-A^{2}-A^{-2}$. Let $M$ be a three-manifold and let $\cal G$ be the set of all isotopy classes of graphs embedded in $M$. We define the Yamada skein module of $M$ as the quotient of the free module $\cal R$$[{\cal G}]$ by the skein relations introduced by S. Yamada to define the topological invariant of spatial graphs known as the Yamada polynomial. In this talk, We compute the Yamada skein module for handelbodies and explore its relationship with the Kauffman bracket skein module (computed by Przytycki and Bullock). In particular, we prove that the Yamada skein module and the Kauffman bracket skein module of the solid torus are isomorphic. We use the skein module of the solid torus to study the $\Z/p\Z$-symmetry of spatial graphs. Namely, we introduce necessary conditions for a spatial graph to be periodic.