In this paper, we consider the symmetric and Hankel-symmetric transportation polytope Ut&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 Ut&h(R,S). Moreover, we show that the extreme points of Ωt&hn, the polytope of symmetric and Hankel-symmetric doubly stochastic matrices, can be obtained from the extreme points of Ut&h(R,S) by specializing to the case that R = S = (1, 1, ..., 1) E Rn.