  In this paper we discuss the Arens regularity of projective tensor product of
Schatten p-class operators. We use the biregularity condition given by \"Ulger
to prove that $S_p(\mathcal H)\otimes^\gamma S_q(\mathcal H)$ is not Arens
regular. We further prove that $B(S_2(\mathcal H))\otimes^\gamma S_2(\mathcal
H)$ is not Arens regular(with respect to usual multiplication) while it is
regular with respect to Schur product. Thus we demonstrate the importance of
biregularity condition given in \cite{Ulger} and the convenience of its use to
prove Arens regularity or irregularity through some concrete examples.
