A protocol for measuring the interaction, deformation and adhesion of soft polymeric substrates with the atomic force microscope (AFM) is described. The technique obtains the photodiode response of the AFM (constant compliance factor) by independent calibration against the rigid substrate adjacent to the deformable particle or patchy film. The zero of separation is taken as the end-point of the jump into contact. A method is given for correcting the velocity dependence of the piezodrive expansion factor, the neglect of which will cause artefacts in dynamic viscoelastic measurements. It is emphasised that conventional force curve analysis, which uses the apparently linear large force region for calibration, will generate erroneous results for deformable substrates. Results are obtained for cellulose particles and for polystyrene films, and their Young's moduli are found to be 22 MPa and 100 MPa, respectively. The latter is about a factor of 30 less than for bulk polystyrene, which indicates that the polystyrene surface is in a less glassy state than the bulk.