Abstract: Let the concentrated forces and the centers of pressure with unknown density functions x(ξ) and y(ξ) respectively be distributed along the axis z outside the solid, then one can reduce an axismmetric loading problem of solids of revolution to two simultaneous Fredholm integral equations. An iteration method for solving such equations is duscussed. A lemma equivalent to E. Rakotch's contractive mapping theorem and a theorem concerning the convergent proof of the iteration method are presented.