The entanglement dynamics involving the so-called entanglement sudden death of atoms in two-photon Tavis-Cummings model is investigated. Various initial conditions that may have influences on the entanglement evolution of atoms, especially on the appearance of atomic entanglement sudden death, are studied. The appearance of entanglement sudden death is sensitive to the initial conditions of the whole system, i.e., the concrete type of atomic initial state, the photon number in the cavity field, and the dipole-dipole interaction between atoms. It is shown that the strong dipole-dipole interaction between atoms can weaken the atomic entanglement sudden death.