In this article, hypergeometric identities (or transformations) for p+1 F p -series and for Kampà e de Fà eriet series of unit arguments are derived systematically from known transformations of hypergeometric series and products of hypergeometric series, respectively, using the beta integral method in an automated manner, based on the Mathematica package HYP. As a result, we obtain some known and some identities which seem to not have been recorded before in literature.