The steady laminar flow of a power-law fluid through a narrow space between two fixed surfaces of revolution, having a common axis of symetry, is considered. To solve this problem the 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 averaged inertia terms 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.