Abstract A geometrically nonlinear model for periodic sandwich structures based on the modified couple stress Timoshenko beam theory with von Karman kinematics is proposed. Constitutive relations for the couple stress beam are derived assuming an antiplane core and then extended for a generic periodic cell. A micromechanical approach based on the structural analysis of a unit cell is proposed and utilized to obtain the stiffness properties of selected periodic sandwich beams. Then, a localization scheme to predict the stress distribution over the faces of the selected beams is defined. The present model is shown to be equivalent to the thick-face sandwich theory for a linear elastic antiplane core cell. Numerical studies validate the present model against three-dimensional finite element models and the thick-face sandwich theory, and compare it with the conventional Timoshenko and couple stress Euler–Bernoulli beam theories. The present model is shown to predict deflections, stresses and buckling loads with good accuracy for different periodic cell setups. The model is able to describe elastic size effects in shear-flexible sandwich beams and the core stiffness influence on membrane and bending stress resultants.