This paper presents a novel mathematical modeling and analysis technique for inductive wireless charging systems. Typically, LC resonance is the most common and basic physical phenomena enabling inductive power transfer (IPT). The work in this paper describes the limitations and inaccuracy of the fundamental harmonic approximation (FHA), which is widely used in the analysis of any resonant based compensation network. Our work introduces a new comprehensive analysis approach for modeling an IPT system, i.e. extended harmonics analysis (EHA), which accounts for the effects of multiple other odd order harmonics on the power transfer, voltage gain, voltage and current stresses on the devices; and hence, provides more accurate design guidelines. As verification of this concept, a laboratory prototype of the wireless charging system is built and tested up to 1 kW and analyzed using both FHA and EHA. It is shown that the deviation of the current estimates from the experimental measurements using EHA is reduced to ~1% from a maximum deviation of ~11% obtained from FHA. Also, the use of EHA modeling has reduced the deviation from experimentally measured voltage gain to 9.6% from 28% in the case of FHA modeling.