We plan to investigate the spatial structure and physical conditions around asymptotic giant brach (AGB)stars (semi-regular variables, Mira stars). Our sample of targets is composed of objects that appear to be in a similar evolutionary stage, judging from the spectral type of the star and the IRAS LRS data. This is necessary to be able to draw more general conclusions. In order to study the spatial structure of the dust shells, we want to map all sources at a wavelength of 50 microns. To date, there exist only IRAS high-resolution maps for some objects with a rather limited quality. It will be the first time that high quality far infrared maps will be produced. To make sure that the shells are sufficiently extended to be resolved by ISO, we have selected our objects from a study that derived the diameter of the dust shells from IRAS data. The diameters are typically several minutes of arc. For all sources IRAS LRS data exist. The IRAS data indicate that a wavelength of 50 microns is ideal to map the envelopes to their full extent. In addition, we wish to measure the near-infrared spectra from 2.5 to 12 microns and the IR spectral flux densities at 70, 90, and 120 microns. We will combine these data with IRAS LRS data to obtain complete spectral energy distributions (SEDs). We have available a radiation transfer programme to model the SED. We have carried out a first successful test for U Orionis (see Fig. 1). The model calculations will allow us to determine the physical parameters of the envelope (e.g. mass, density and temperature distribution).