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Bi-directional Inductive Power Transfer (IPT) systems allow contactless power transfer between two sides and across an air-gap, through weak magnetic coupling. These systems essentially constitute high order resonant circuit and their complexity increases with increasing number of pick-ups. A mathematical model which provides an insight into the behaviour of bi-directional IPT systems with multiple pick-ups would therefore be invaluable at design stage. This paper develops a multivariable dynamic model for bi-directional IPT system with multiple pick-ups. A 1.5 kW bi-directional IPT system with 3 pick-ups is simulated in PLECS and the results are presented with comparisons to demonstrate the validity of the proposed model. Results of the simulation indicate that the proposed model accurately predicts the behaviour of bi-directional IPT system with multiple pick-ups and can therefore be used as a valuable tool for both dynamic analysis and controller design.