After briefly introducing Akhtarshenas, concurrence vector and subvector for describing many-body entanglement,we investigate the entanglement formation for a system which contains three bodies, i.e. two identical atoms and a single model cavity field, in the Tavis-Cummings model by calculating the concurrences. The results show that the coupling strength between two atoms, the decay cavity and the atomic spontaneous emission can change the entanglement of formation according to different modes: these factors destroy periodicity and symmetry of all concurrences, and that the coupling strength of two atoms does not change the peak value of concurrence (C), but the strength of decay cavity and the atomic spontaneous emission decline in the peak value of concurrence (C) and the latter is more serious than the former under the same strengths. The concurrence vector and subvector are a useful measure of entanglement for a pure state of the many-body system, in that it can give novel pictures about the entanglements for the entire system and between its inner bodies.