A steady laminar diffusion flame burning in the core of a vortex is studied. Solutions of the full Navier‐Stokes equation and the mass‐transfer equation are obtained to study the effect of the swirling motion on the flame and its flow field for different values of the Schmidt number. The flow conditions depend on two parameters:&Ggr;∞, the circulation of the vortex and Re, the Reynolds number based on the velocity at the axis of symmetry. The velocity distribution is strongly affected by the circulation. As&Ggr;∞increases when Re remains constant the width of the jet flow in the core region also increases. However, the mass concentration distribution and the position of the flame depend principally on Re, and on&Ggr;∞only slightly.