  The connective constant $\mu(G)$ of a graph $G$ is the asymptotic growth rate
of the number $\sigma_{n}$ of self-avoiding walks of length $n$ in $G$ from a
given vertex. We prove a formula for the connective constant for free products
of quasi-transitive graphs and show that $\sigma_{n}\sim A_{G} \mu(G)^{n}$ for
some constant $A_{G}$ that depends on $G$. In the case of finite products
$\mu(G)$ can be calculated explicitly and is shown to be an algebraic number.
