The authors conducted a numerical investigation of the laminar flow issuing from a methane/air coaxial burner submitted to a magnetic field. They intend to understand the mechanisms involved in the magnetic stabilization of the lifted flames. The model is based on the coupled equations of conservation of mass, species, and momentum in which the magnetic force acting on paramagnetic oxygen is introduced in the source term. A CFD code is used to solve the steady-state equations in an axisymmetric domain. Air jet velocity is shown to decrease locally in front of the magnetic gradient. Calculation of the stoichiometric radius reveals a lateral displacement of the stoichiometric line and a decrease of the fuel mass fraction gradient when the magnetic force is applied. These results explain the observed reduction of the liftoff height of flames under magnetic gradient due to an increase of the flame propagation velocity.