A 3D model for the simulation of inductively coupled plasma torches (ICPTs) working at atmospheric pressure is presented, using a customized version of the computational fluid dynamics (CFD) commercial code FLUENT^®. The induction coil is taken into account in its actual 3D shape, showing the effects on the plasma discharge of removing the axisymmetric hypothesis of simplification, which characterizes 2D approaches. Steady flow and energy equations are solved for optically thin argon plasmas under the assumptions of local thermodynamic equilibrium (LTE) and laminar flow. The electromagnetic field equations are solved on an extended grid in the vector potential form. In order to evaluate the importance of various 3D effects on calculated plasma temperature and velocity fields, comparisons of our new results with the ones obtainable from 2D models and from an improved 2D model that includes 3D coil effects are presented. 3D results are shown for torches working under various geometric and operating conditions and with different coil shapes, including conventional helicoidal, as well as planar, elliptical, and double-stage configurations.