This study develops a geometrically nonlinear model of a wind turbine blade utilizing finite strain theory for the calculation of elastic forces. The model is based on the floating frame of reference (FFR) formulation, which is a common choice in the modeling of long and flexible wind turbine blades. To model the nonlinear deformation of blades, the FFR formulation divides the structure into several substructures, which involves a significant increase of the system degrees of freedom. In the presented model, a nonlinear description of the elastic forces is introduced to achieve the convergence of the dynamic blade model at a lower number of substructures. The nonlinear elastic forces are formulated according to the Euler-Bernoulli beam theory, and they account for third-order terms of the potential elastic energy, the so-called geometric stiffness. The developed blade model is formulated in two dimensions and tested in a blade of 44.8 m length, which corresponds to a 2.75 MW wind turbine. Firstly, the results show that linear models do not accurately represent tip blade transverse displacement, and the substructuring technique becomes necessary to account for geometric nonlinearity. Secondly, using nonlinear elastic models significantly reduces the number of substructures needed to achieve convergence of the solution.