We study the hydrodynamical behavior of the gas expelled by moving asymptotic giant branch stars interacting with the interstellar medium (ISM). Our models follow the wind modulations prescribed by stellar evolution calculations, and we cover a range of expected relative velocities (10-100 km s-1), ISM densities (between 0.01 and 1 cm-3), and stellar progenitor masses (1 and 3.5 M &sun;). We show how and when bow shocks and cometary-like structures form, and in which regime the shells are subject to instabilities. Finally, we analyze the results of the simulations in terms of the different kinematical stellar populations expected in the Galaxy.