A hydrostatic model atmosphere of a typical umbral core is constructed on the basis of both Na I D 2 line profile and umbral core-to disk continuum intensity ratio. The observations were obtained by Mullan and Wyller with photoelectric means over the range from 4000 |AA a n d 6500 |AA . The computed line profile of Na I D 2 and the emergent continuum intensity distribution are compared with the observations. The temperature of umbral cores is found to be lower by 300 ˚ K t o 500 ˚ K than that of their ambient umbral region. The detailed physical structure of a working model of umbral cores is proposed.