We consider the Feynman amplitudes for all the essentially and crossed planar graphs of the four‐point vertex function in φ3 field theory, and we evaluate their behavior at high energy (large s, fixed t). We compute the coefficients of all logarithms for the dominant amplitudes which behave in s −1 (up to logarithms of s). This computation is performed by using the Bogoliubov–Parasiuk–Hepp R operation and the Mellin transform of the Feynman amplitudes. The geometrical structure of the coefficients is such that all logarithms of s of all dominant amplitudes can be summed to give the well‐known Regge behavior with signature +. The Regge trajectory verifies an equation which may be solved explicitly in the lowest order approximation; the residue is found to be the ratio of two functions of t, the upper one being factorized into two vertex functions expressed as infinite series and the lower one providing a ghost killing factor.