Using the language of Seshadri stratifications we develop a geometrical interpretation of Lakshmibai-Seshadri-tableaux and their associated standard monomial bases. These tableaux are a generalization of Young-tableaux and De-Concini-tableaux to all Dynkin types. More precisely, we construct filtrations of multihomogeneous coordinate rings of Schubert varieties, such that the subquotients are one-dimensional and indexed by standard tableaux.