The role of flexoelectric properties in arising of the electric field induced periodic deformations of nematic planar layers, known as longitudinal domains, was determined numerically. Rigidly anchored insulating nematic was considered. Both signs of dielectric anisotropy were taken into account. The structure of the domains was determined. The threshold voltages for arising of the domains and their initial spatial period were calculated as functions of dielectric anisotropy and of elastic constants ratio k22/k11, for various values of the difference of flexoelectric coefficients |e11 - e33|. The ranges of these parameters, for which the domains exist, were determined.