LS 5039 is a gamma-ray binary system hosting a compact object and a massive O-type stellar companion. It presents a broadband emission spectrum that goes from radio up to gamma rays with energies of a few dozen TeV. In one of the proposed physical scenarios, the compact object is a non-accreting pulsar and the non-thermal radiation comes from an outflow produced by the interaction of the pulsar and stellar winds. We present a semi-analytical model that computes the dynamical evolution of this outflow, as well as its expected non-thermal emission. We compare the model results with the existent data of LS 5039, paying special attention to the extended and time-dependent radio structures observed in the source.