Fragmentation of small sodium clusters was studied by performing both ab initio and classical molecular dynamics simulations. In ab initio calculations at 1200-2400 K, neutral sodium clusters with 10 and 13 atoms ejected both monomers and dimers. The observed behavior is in agreement with previous calculations stating that the electronic shell oscillations diminish strongly as a function of temperature. The fragmentation rates obtained with the ab initio method are consistent with the Kelvin equation for the equilibrium vapor pressure of small clusters. The differences between the results obtained using different models reflect the differences between the dissociation energies calculated correspondingly.