A mathematical model is proposed for the dissolution of stoichiometric particles in binary alloys occurring during the heat treatments of as-cast aluminium alloys prior to hot extrusion. The Level Set method is used to capture the interface location implicitly. The front velocity, only dened on the moving interface, should be advected to the whole computational domain. This advection is done in Cartesian or in normal directions. The numerical solution is carried out by a combination of finite difference and finite element methods. The cut-cell method is employed to adapt the nite element mesh to the interface position. Two- and three-dimensional results are presented. The numerical solution is compared with analytical solutions. Conservation of mass is also evaluated.