Abstract In order to analyse the convective instability of the force-free magnetic field, an exact solution of the MHD equation for the magnetic field (1) together with the flow field (2) of constant speed V 0 making an angle θ with the magnetic field, was chosen as the unperturbed state. The stability of the fields between two parallel conducting walls of seperation d was studied by a linear perturbation method, which led to the eigenvalue problem (12), X being given by (13). It was shown by an approximate variational method that instability will set in by the flow field if V 0 is greater than 1/ 3 times Alfven velocity V A. For β= V 2 o V 2 A < 1 3 , the stability of the force-free field (1) is not influenced by the flow field, which may still be significant in other respects. Perturbations transverse to the magnetic field were found to be the most unstable modes.