Earlier presented the geometrically nonlinear model of a flexible beam (cylindrical bending of a plate) was used for analysis of post-buckling behavior of the layered composite with delamination at compression. In this paper the model is used for more details nonlinear analysis of double cantilever beam (DCB) that used in standard test for determination of the interlaminar fracture toughness composites with delamination-type damage. The main advantage of the model is a precise description of the curved axis of the beam (plate) without linearization or other higher order approximations. The exact solution of bending differential equation finally can be expressed in terms of the incomplete elliptic integrals of the first and second kind. The model describes only geometrically nonlinear effect of DCB arms bending (global effect) and should be combined with the procedure of effective delamination extension to correct DCB arms rotation at delamination front (local effect). First of all the nonlinear model can serve as a tool to estimate the possible error due the geometrical nonlinearity in comparison with linear solution. On the other hand, this model can be effectively used to determine interlaminar fracture toughness using DCB samples at large deflections. Validation of the model is made using data of standard tests of glass/epoxy DCB samples.