The present work aims at comparing different coupling coils by taking into account sources of uncertainty for static inductive power-transfer (SIPT) systems. Due to the maximum transmission efficiency for the SIPT system related to the mutual inductance between coils, the key point here is to make use of a sparse polynomial chaos expansion (PCE) method to analyze the mutual inductance between the transmitter and the receiver. A fast postprocess-sensitivity analysis allowed the identification of which source of uncertainty was the most influential factor to the mutual inductance for different coupling coils. Furthermore, in view of the relationship between the maximum transmission efficiency and the ratio of the length of wires of a coil and the mutual inductance, circular coupling coils should be recommended for SIPT systems.