A numerical model for simulating air and nitrogen inductively coupled plasmas (ICPs) was developed considering thermochemical nonequilibrium and the third-order electron transport properties. A modified far-field electromagnetic model was introduced and tightly coupled with the flow field equations to describe the Joule heating and inductive discharge phenomena. In total, 11 species and 49 chemical reactions of air, which include 5 species and 8 chemical reactions of nitrogen, were employed to model the chemical reaction process. The internal energy transfers among translational, vibrational, rotational, and electronic energy modes of chemical species were taken into account to study thermal nonequilibrium effects. The low-Reynolds number Abe-Kondoh-Nagano k-epsilon turbulence model was employed to consider the turbulent heat transfer. In this study, the fundamental characteristics of an ICP flow, such as the weak ionization, high temperature but low velocity in the torch, and wide area of the plasma plume, were reproduced by the developed numerical model. The flow field differences between the air and nitrogen ICP flows inside the 10-kW ICP wind tunnel were made clear. The interactions between the electromagnetic and flow fields were also revealed for an inductive discharge. Published by AIP Publishing.