Electric field-induced deformations in hybrid aligned layers of nematic liquid crystals possessing flexoelectric properties were investigated numerically. The thresholdless one-dimensional deformations occurred at low voltages whereas the spatially periodic deformations, taking the form of parallel stripes, were found above sufficiently high threshold voltage. The threshold voltage decreased when the flexoelectric properties get stronger. The stripes were parallel to the direction of planar alignment. The director distributions in the stripes induced by positive voltages differed qualitatively from those arising at negative voltage. The evolution of deformations during increase of bias voltage was investigated. The role of flexoelectric properties and of dielectric anisotropy was studied. The spatial period of deformations shortened with increasing voltage and with increasing flexoelectric coefficients.