Abstract <p>The nonlinear model of size-dependent magneto-electro-elastic (MEE) laminated Timoshenko nanobeam is established by considering the effects of von Karman nonlinear theory, two-parameter Winkler–Pasternak foundation, nonlocal strain gradient theory (NSGT) and flexomagnetoelectric (FME) effect. The nonlinear differential equation of MEE laminated nanobeams is acquired by means of the Hamiltonian principle, and the Galerkin method is employed to truncate it. In the numerical simulations, the influences of Winkler–Pasternak foundation parameters, scale parameters, FME effect, external electric potential and external magnetic potential on the bending characteristics of MEE laminated nanobeams are qualitatively examined and contrasted with the related literature. Results show that the FME effect slightly reduces the maximum deflection of the nanobeam. It is affected by multiple parameters, among which the influence of scale parameters is prominent. In engineering applications, attention should be paid to the influences of factors such as high span ratio and lamination sequence.</p>