This paper presents a new structure of an induction heater for aluminium parallelepiped workpiece. The studied device uses a magnetic field created by a permanent magnets (PM) inductor (Halbach inductor) in which the conducting workpiece is subjected to a linear oscillatory motion with alternating velocity. An analytical electromagnetic model is developed to find the induced heating power in the workpiece. To consider the transverse edge effect, an analytical corrected model is also presented. The most important results obtained by these models are verified experimentally on a prototype. Index Terms-, analytical model, oscillatory linear motion, permanent magnet, transverse edge effect. 0018-9464 (c)