Summary: In this paper, we consider the symmetric and Hankel-symmetric transportation polytope \(\mathcal U^{t \& h}(R,S)\), which is the convex set of all symmetric and Hankel-symmetric non-negative matrices with prescribed row sum vector \(R\) and prescribed column sum vector \(S\). We characterize all extreme points of \(\mathcal U^{t \& h}(R,S)\). Moreover, we show that the extreme points of \(\Omega_n^{t \& h}\) the polytope of symmetric and Hankel-symmetric doubly stochastic matrices, can be obtained from the extreme points of \(\mathcal U^{t \& h}(R,S)\) by specializing to the case that \(R=S=(1,1,\ldots,1) \in \mathbb R^n\).