Wireless Power Transfer System (WPTS) is gaining more attention across low power to high power applications. It is a convenient, safer, reliable, and user-friendly solution to wireless Electric Vehicle (EV) charger users. In WPTS, large air-gap between coils may cause high leakage of magnetic fields and it may also lower the coupling factor (k). In such systems, selection of coil structure and core configuration plays a key role to reduce the magnetic leakage. In this paper, a thorough mathematical analysis of various coil structures has been presented and observed the change in inductance from one coil structure to another. A finite element method is used in this paper to study the effect of coil structure on self-inductance, mutual inductance and coupling factor between the coils. This paper also provides the numerous core configurations, which have been added to WPTS and simulated to find its effect on power transfer efficiency between transmitter and receiver. The analysis on various coil-core configurations are performed for distinct air gaps between the transmitter and the receiver and found the supreme coil-core configuration to achieve the better coupling between them. © 2017 IEEE.