The attenuation mean free path, lambda att, of nucleons and pions in thick lead chambers is calculated assuming a simple geometrical model for hadron-nucleus interactions and also taking experimental procedure into consideration. The results are compared with experimental data of the Pamir and Chacaltaya collaboration experiment, where it is observed that lambda att of hadrons in high-energy families is much smaller than that of ordinary hadrons. lambda att of single-arrived hadrons, which are considered to be mostly protons, observed in the same experiment, agrees well with calculations for proton incidence. For hadrons in families, however, calculations give lambda att not smaller than that of single-arrived hadrons and fail to explain the experimental results even when we assume hadrons are mostly nucleons in high-energy families. Fluctuations in the estimation of lambda att are also discussed.