We have used the atomic force acoustic microscopy (AFAM) method to determine the indentation modulus of nanoporous thin-film materials with ultralow values of dielectric permittivity (dielectric constant k < 2.4). The AFAM method is based on the contact mode of atomic force microscopy (AFM) and as such is able to characterize materials with high spatial resolution. The tested material was porous organosilicate glass with nominal porosity ranging from 27% to 40%. The values obtained for the indentation modulus varied from 4 to 7 GPa depending on the pore concentration. The values obtained for the indentation modulus by use of the AFAM method were in very good agreement with those determined by nanoindentation. In addition, a part of the AFAM results obtained for the sample with the highest porosity content showed dependence of the effective indentation modulus on the applied load. Preliminary data analysis suggests that the stress rate is the critical factor in triggering this particular mechanical response of the porous material.