The present work focuses on the study of non-equilibrium effects in radio frequency inductively coupled plasmas (ICP) using state-of-the-art state-to-state models. The fluid governing equations are discretized in space based on a cell-centered finite volume method. A preconditioned compressible formulation is adopted to tackle the stiffness resulting from low Mach numbers. Non-Local Thermodynamic Equilibrium (NLTE) calculations are performed using either multi-temperature or state-to-state models. Electromagnetic equations are solved via the finite element method, where H(curl) and H(Div) conforming finite element spaces are used for the electric and magnetic fields, respectively. Two solvers, one for the fluid and the other for the electromagnetic phenomena are coupled in an explicit fashion to model NLTE ICP discharges. Simulations performed using electronic state-to-state model show a significant deviation of the populations from the Boltzmann distribution.