An experimental investigation of track densities, due to cosmic ray nuclei, has been carried out in samples taken from the exterior faces of about 160 meteorites. This information, together with the exposure ages of these meteorites, was used to determine the “shielding” depths of the samples in space. The distributions of shielding depths, coupled with sampling documentation, enable us to classify meteorites in four distinct ablation classes. These data are then used to determine preatmospheric masses of meteorites. Depending on the adequacy of track-sampling and the type of ablation, “good”, “model” or “limit” estimates have been made of the preatmospheric masses of the meteorites. Good estimates were obtained for 27 meteorites, model estimates for 49 meteorites, and lower limits for 34 cases. No ablation estimates were obtained in 55 cases, because of lack of adequate sampling. The following results are secured: 1. (1) Mass ablation estimates range between 27% and 99.9% with a weighted mean (or median) ablation of about 85%. The preatmospheric masses ( M 0) of the meteorites studied fall predominantly into the mass interval 10–1000 kg, with a distribution d N ∝ M 0 −1 d M 0. 2. (2) Even in cases of large mass ablation (> 90%), regions of low ablation (5–7 cm) are frequently found. This is due to the statistical survival of exterior fragments, in the case of showers or due to asymmetric ablation. 3. (3) A relation is observed between the preatmospheric mass of the meteorite, the track production rate (TPM) and spallogenic 22Ne/ 21Ne ratios in “shielded” samples. The data base used in this analysis are measurements of track densities and spallation 22Ne/ 21Ne (NeR) ratios in aliquot samples. This empirical relation can be used to determine the preatmospheric masses of meteorites from track and NeR data of a few interior samples. 4. (4) A statistical analysis of our data, in conjunction with the known velocity distribution of meteors producing bright fireballs, suggests a relationship between mean mass ablation and atmospheric velocity of the meteorite for a range of 14–20 km s −1. If such a relationship holds, approximate orbital elements could, in principle, be determined where information is available on the visual observations of the radiants.