The effect of free-streaming axion emission on numerical models for the cooling of the newly born neutron star associated with SN1987A is considered. It is found that for an axion mass of greater than approximately 10 to the -3 eV, axion emission shortens the duration of the expected neutrino burst so significantly that it would be inconsistent with the neutrino observations made by the Kamiokande II and Irvine-Michigan-Brookhaven detectors. However, the possibility has not been investigated that axion trapping (which should occur for masses greater than or equal to 0.02 eV) sufficiently reduces axion emission so that axion masses greater than approximately 2 eV would be consistent with the neutrino observations