Among various kinds of mechanical parts, there is no other element that is characterized by a large elastic deformation as the spring. With parts featuring such large elastic deformation, the treatment of its geometrical nonlinearity stands out as a most vital matter, for which it will be important to express the deformed shape precisely. In this context, when analyzing springs by the finite element method (FEM), the use of a high-order isoparametric element appears appropriate, so we developed such an element for curved and twisted beams. But there are many kinds of springs which can be treated as two dimensional problem. Naturally, it would be irrational to solve two dimensional problems in three dimensions. This report deals with a high-order isoparametric element, limiting our discussion to the bending of beams having only plane curvature. The fundamental thought is based on the theory described in Ref. 1) in which the curvature and the cross-sectional size are variable in one element, so this method may be applicable to long tapered beams. As an example, we apply the element to spiral springs, and introduce an up-dated Lagrange method to solve geometrically non-linear problems.