We have investigated the dynamical interaction of low- and intermediate-mass stars (from 1 to 5 Msolar) with their interstellar medium (ISM). In this first paper, we examine the structures generated by the stellar winds during the asymptotic giant branch (AGB) phase using a numerical code and the wind history predicted by stellar evolution. The influence of the external ISM is also taken into account. We find that the wind variations associated with the thermal pulses lead to the formation of transient shells with an average lifetime of ~20,000 yr and, consequently, do not remain recorded in the density or velocity structure of the gas. The formation of shells that survive at the end of the AGB phase occurs via two main processes: shocks between the shells formed by two consecutive enhancements of the mass loss or continuous accumulation of the material ejected by the star in the interaction region with the ISM. Our models show that the mass of the circumstellar envelope increases appreciably because of the ISM material swept up by the wind (up to ~70% for the 1 Msolar stellar model). We also point out the importance of the ISM on the deceleration and compression of the external shells. According to our simulations, large regions (up to 2.5 pc) of neutral gas surrounding the molecular envelopes of AGB stars are expected. These large regions of gas are formed from the mass loss experienced by the star during the AGB evolution.