Paper-based materials are being alternative candidates to build load-bearing components for the high demanding building sector to be committed to the green transition, but more knowledge of structural mechanics of such components is needed. In this work, three categories of innovative load-bearing sandwich beams with cup-box core fully made of different paper materials were produced, tested and analyzed in four-point bending. The first failure mode was observed at the top facesheets due to the low compressive strength of paper materials; Beams with thin facesheets had premature buckling failure, whereas those with thicker facesheets exhibited ductility reaching higher deflection before the compressive failure. The developed finite element model, calibrated with the experiments for the equivalent bending and shear rigidities, provided figures of the modulus of the facesheet as well as the properties of the core. Furthermore, the compressive plasticity behavior of the facesheets was assessed by fitting the model with load-deflection curves from the tests. Using the model for the structural optimization of the thickness and height of the core, the work suggests optimal values 3 times higher than the original ones.