This paper presents the results of modeling the lower ionosphere response to solar X-ray flares of C-, M- and X-classes. The model is based on a 5-component scheme of the ionization-recombination cycle of the ionospheric D-region. Input parameters of the plasma-chemical model under different heliogeophysical conditions corresponding to selected X-ray flares were determined by using data received from AURA, SDO and GOES satellites. Verification of the obtained results was carried out with use of ground-based radiophysical measurements taken at the geophysical observatory Mikhnevo. Results of comparing the calculated and experimental the radio wave amplitude variations along six European very low frequency (VLF) paths show that the root mean square error (RMSE) does not exceed 1.5 dB for ~70% of cases including X-class flares during which the amplitude jump on some paths reaches 8 dB. Qualitative and quantitative analysis of the verification results of the VLF signal amplitude has showed the good predictive capability of the built model for describing weak and moderate ionospheric disturbances.