Stopping powers of alpha particles have been measured for CO2, O2, N2, and CH4 over an energy range from 0.1 to 5.3 MeV. From these measurements atomic stopping cross sections of alpha particles in tissue (H, 10.1%; C, 12.1%; N, 4.0%; O, 73.6% by weight) have been evaluated. For energies less than 1 MeV the results are as much as 50% higher than those calculated by Neufeld and Snyder, assuming that the stopping power of an ion is given by the product of the proton specific stopping power and the average of the square of the charge of the ion. Possible explanations are presented to account for this discrepancy.