The primary purpose of the present study was to elucidate the role of mesopores of Y zeolites in the hydrocracking of large molecules, such as heavy oils. For this purpose, two kinds of HY zeolites, one with and one without mesopores, were prepared by ion exchange of two NaY zeolites with different Si/Al ratios. Their catalytic activities were then evaluated by the hydrocracking of two model compounds, each having a different molecular size. In the hydrocracking of diphenylmethane, which has a smaller molecular size and thus can diffuse into micropores, the two HY zeolites exhibited similar catalytic activities. On the other hand, in the hydrocracking of triphenylmethane, which has a larger molecular size, the HY zeolite with mesopores gave almost four times higher reaction rates as compared with the HY zeolite without mesopores. This higher activity was because the larger molecular size limits the catalytically active sites to those only on the external surface including the mesopore surface of the HY zeolite particles. These results indicate that the catalytic activities over the total surface and over the external surface can be estimated using two model reactions, each involving a compound that has a different molecular size.