To study the large displacement and large rotation problems, geometrically nonlinear formulation of eccentric degenerated beam element has been developed, where the restrictions of infinitesimal rotation increments are removed and the incremental equations are derived using the Taylor series expansion of the displacement function at time t+dt. The geometrically nonlinear analyses are carried out for the cases of cantilever, square frame, shallow arch and 45-degree bend beam and all of them are compared with each of the other results published. The element developed in the present research can be efficiently utilized for analysis of the nonlinear behaviours of structures when displacements and rotations are large.