The strain gradient magnetoelectroelasticity is applied to solve two-dimensional boundary value problems. The electric and magnetic field-strain gradient coupling is considered in constitutive equations. The meshless local Petrov-Galerkin (MLPG) is developed to solve general problems. All field quantities are approximated by the moving least-squares (MLS) scheme. Effective material properties for a piezomagnetic matrix with regularly distributed piezoelectric fibres of a circular cross section and coating layer are presented.