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Brownian dynamics simulation is conducted for a dilute surfactant solution under a steady uniaxial elongational flow.A new inter-cluster potential is used for the interaction among surfactant micelles to determine the micellar network structures in the surfactant solution.The micellar network is successfully simulated.It is formed at low elongation rates and destroyed by high elongation rates.The computed elongational viscosities show elongation-thinning characteristics.The relationship between the elongational viscosities and the microstructure of the surfactant solution is revealed.