Axisymmetric nozzle flows with a free-jet expansion are simulated considering several substances and several flow conditions, and the thermophysical properties in the nozzle and the free-jet region are predicted. The present numerical method is based on the preconditioning method developed by Yamamoto and the mathematical models of thermophysical properties of the substances. As numerical examples show, gas flows of carbon dioxide, water, and nitrogen under a subcritical pressure condition are first calculated. Calculated distances to the Mach disk are compared with the experimental results, and also the density distributions are compared among these three substances. Second, carbon dioxide flows while changing the pressure from subcritical to supercritical values are calculated and the effect of pressure on the flow field is investigated. Third, flows of water vapor with and without nonequilibrium condensation are calculated and the effect of condensation on the flow field is investigated. (C) 2010 American Institute of Chemical Engineers AIChE J, 57: 2629-2635, 2011