The present paper studies the (dp) stripping reactions with the target core excitation. In this case, we assume that the target nucleus and the residual nucleus contain the conventional shell model configuration and other configurations mixed by the nucleon-nucleon residual interaction.We derive the differential cross section formula for the reaction process based on the above assumption. The formula shows that the contribution to the reaction cross section is mainly due to the configuration mixing of target nucleus. We may expect that the cross section values are rather small, because the admixture in general is weak. The formula also shows that the characteristic peak of the reaction angular distribution is determined by the orbital angular momentum quantum number of the hole state which is created during the core excitation. These two conclusions are consistent with experimental results for this type of reactions.We apply this formula to calculate the "spectroscopic factors" for six reaction events. The theoritical values of the "spectroscopic factors", within the experimental errors, agree with those extracted from the experimental data.