In this study, a series of linear- and long-chain branched polylactic acid (PLA) samples was prepared by electron beam irradiation without or with addition of a trifunctional monomer, trimethylolpropane triacrylate (TMPTA). The chain structures of the PLA samples were characterized by size-exclusion chromatography coupled with a light scattering detector (SEC-MALLS) and shear and extensional rheology. PLA tends to degrade while keeps linear structures with increasing irradiation dose and without addition of TMPTA, as evidenced by decreased molecular mass M(w) and reductions of storage modulus G' and the zero shear viscosity eta'. Long-chain branched PLA samples were successfully prepared with irradiation and addition of TMPTA, which shows prominent higher eta(0) and apparent flow activation energy, longer characteristic relaxation time tau, and pronounced strain-hardening behaviors. With increasing amount of TMPTA, M(w) dependences of eta(0) and the root mean square radius of gyration R(g) obviously deviate from the scaling relation of linear PLA samples, which strongly indicates the increased long-chain branching degree for the branched PLA samples. (C) 2011 Wiley Periodicals, Inc. J Appl Polym Sci 122: 1857-1865, 2011