In this note, Föppl-Hencky membrane equation in the case of axisymmetric deformation was derived, and its power series solution was presented by using the displacement-based solution method. The result shows that both the displacement-based solution method and the stress-based solution method are effective for the solution to Föppl-Hencky equation. But in comparison with the latter, the former makes the solving process some more concise. In addition, some issues concerned were also discussed.