Abstract The paper discusses governing differential equation for determining large deflections of slender, non-homogeneous beam subjected to a combined loading and composed of a finite number of laminae, which are made of nonlinearly elastic, modified Ludwick's type of material with different stress–strain relations in tension and compression domain. The material properties are varying arbitrarily through the beam's thickness. When the thickness of laminae is sufficiently small and the variation of mechanical properties is close to continuous, the beam can be considered as made of functionally graded material (FGM). The derived equations are solved numerically and tested on several examples. From a comparison of the results obtained and those found in the literature a good agreement was observed.