The electro-vortex flow is a very important phenomenon, taking place in the different processes in metallurgy, such as electrical welding or electrical melting. It appears in the conducting medium under the action of the electromagnetic force due to interaction of the non-uniform electrical current (which passes through this medium) and self-magnetic field. Here we present the study of the electro-vortex flow for the hemispherical geometry. The equations were solved in variables "vorticity – vector potential of velocity". We considered the problem using Stokes approximation and non-linear case with a finite size of the central electrode, and compared the results obtained by different methods of solving the equations.