Plate structures are often subjected to differential compression due to non
uniform bending during their service life. In practice, most beams are subj
ected to transverse loads that create moment gradient; the resulting loadin
g system for such beams is a combination of longitudinal stress gradient wi
th associated shearing and transverse stresses. This paper presents a theor
etical view of elastic local instability of anisotropic composite beams whi
ch are treated as assemblies of symmetric angle-ply composite plates buckli
ng under nonlinear varying, uniaxial compressive forces. Uniformly distribu
ted load and central concentrated load are two common loading systems actin
g on simply supported, wide-flange I-section beams. The Galerkin method is
applied to the resulting plate equilibrium equations. The present study sho
ws that the buckling load obtained from the proposed approach for composite
flanges is greater than that obtained by existing solutions. Results also
show that for beams subjected to the uniformly distributed load loading sys
tem, local buckling may be initiated in the web, especially for short-span
deep beams. However, under the central concentrated load loading system, th
e compressive flange limits buckling strength.