The subject of this article is the finite element method (FEM) simulation of the multi-layered rectangular composite beam subjected to three-point bending test. The study is focused on the composite beams made of glass or carbon fibre-reinforced laminates (glass fibre-reinforced polymer [GFRP] and carbon fibre-reinforced polymer [CFRP]) for which different laminate stacking were addressed. Three beam geometries with various length-to-thickness ratios included short beam shear (SBS) test, provided the beam is short relative to its thickness, which maximised the induced shear stresses. Simulation included the application of Tsai–Hill, Hoffman, Tsai–Wu, Hashin and Puck failure criteria to perform the composite beam failure analysis wherein the matrix and fibre failure were considered separately. Numerical failure studies also aimed to verify the beam failure modes and the participation of stress tensor elements in material failure.