The stress distribution in plates fabricated from the multilayered composite materials with periodical small-scale curved structures has been studied. It is supposed that the continuously distributed normal forces act on the upper plane of the plate. Moreover, it is assumed that the plate is simply and rigidly supported at opposite sides. The investigation has been carried out in terms of the three-dimensional theory of elasticity, while the mechanical relationships of the given plate material have been described by the Akbarov and Cuz' continuum approach. The numerical results obtained with the use of the semianalytical FEM show that the curving in the plate material structure affects the stress distributions in this plate.