In this paper, miniaturized multilayer rectangular printed circuit board (PCB) coils are investigated and, a method for calculating the total self-inductance, mutual inductance, and power transfer efficiency between two miniature (6.6mm x 6.6mm) coils for wireless power transfer applications is presented. First, in order to reduce the complexity, coil trace turns are modeled as rectangular loops. A formula based on integral solution starting from Biot - Savart's law gives the analytical results of the mutual inductances between each rectangular trace in same and different layers. Then 4-layer rectangular PCB coil based wireless power transfer system is modeled, analyzed and simulated. Mutual inductance and power transfer efficiency parameters according to the distance between coils and trace width of the coils are calculated with analytical methods. Achieved inductance and power transfer efficiency results from the analytical model and simulation results in Ansys - Maxwell and Simplorer environment is compared for verification. The analytical approach proposed in this paper is provide a fast mutual inductance and power transfer efficiency calculation for multilayer rectangular printed circuit board inductors compared to the simulation.