Abstract: The absolute nodal coordinate formulation(ANCF) was widely used in the research of multi-body dynamics. But the thin plate element which designed for modeling thin shell structure couldn't be adopted for initial curved structure directly because of its deficiency of position vector gradient. Thin plate element was chosen for modelling the leaf spring to avoid the troublesome locking problem when using fully parameterized ANCF element. One explored the way to express the elastic force of existing thin plate element via common continuum mechanics system by adopting the unitized normal vector on the centroid plane as the added position vector gradient for thickness direction. So as to modify its elastic force formulation. The completed form of the element was given which could eliminated the introduced initial stress when describing initially curved leaf using the standard procedure which could only be performed on fully parameterized ANCF element. The modification for elastic force would not affect the element property. By setting undeformed structure which differs from initial one, the controlled initial stress could be introduced into the model for describing the assemble process. Numerical results were given to verify the validity of this modification. An initial curved double-leaf spring model was built. In order to specify the exact contact region, a cross element search strategy using a local material coordinate system built on the entire leaf was developed. Introduced a more precise calculation procedure for contact and friction force using penalty method and smooth Coulomb law. The rigid-flexible coupled leaf spring model combined with ANCF reference nodes was built, integrated with shackle, chassis and their mechanism movement.