A Riemannian manifold \(M\) with a metric \(g\) is Einstein if its metric \(g\) satisfies the equation: \(\text{Ric}(g)=Cg\), where Ric is the Ricci tensor of \(M\) and \(C\) is a constant. Let \(G\) be a connected, compact simple Lie group and \(H\) its closed simple subgroup with \(G/H\) simply connected. The homogeneous Riemannian metric induced on \(G/H\) by the Killing form of the Lie algebra of \(G\) is referred to as the standard homogeneous metric. In this paper, the author gives a complete classification of compact, simply connected, standard homogeneous, periodic Einstein manifolds, i.e. manifolds whose transitive groups of motions are not simple, but instead, at each point of a manifold there exists a symmetry of finite order. It turns out that each such manifold is isometric to a symmetric, compact space or to the Riemannian product of spaces of special type.