The meshless local integral equation method is developed to analyze general two-dimensional boundary value problems in size-dependent magnetoelectroelastic solids. A consistent theory is developed for size dependent magnetoelectroelasticity. The strain gradients are considered in the constitutive equations for electric displacement and magnetic induction. The governing equations are derived with the corresponding boundary conditions using the variational principle. The local integral equations are subsequently derived and the meshless moving least square (MLS) numerical method is implemented to solve these equations.