In 1956 Kassel obtained his habilitation at the University of Würzburg with a thesis on Greek and Roman consolation literature.
[1] In 1975 Kassel moved to the University of Cologne where he became professor of Ancient Greek philology at the Institut für Altertumskunde.
[2][3] Amongst his academic output Kassel published work on Poetics and Rhetoric by Aristotle, Ancient Greek comedy and Menander.
Together with Colin François Lloyd Austin he published an edition of the fragments of ancient Greek comedy in eight volumes under the title Poetae Comici Graeci.
[2] He was considered an expert on papyrology and epigraphy and served as co-editor of the Zeitschrift für Papyrologie und Epigraphik.