The steady laminar MHD now of a viscous fluid in the presence of azimuthal magnetic field is considered, through a narrow space between two fixed surfaces of revolution, having a common axis of symmetry. To solve this problem the MHD boundary layer equations are used and expressed for the axially symmetric case in a curvilinear orthogonal coordinate system x, theta, y connected with one of the surfaces. The method of asymptotic solution is used to solve the boundary layer equations. As a result one obtains the formulae expressing such flow parameters as the velocity components v(x), v(y) and the pressure p.