Making use of the arbitrary shock theory developed by Ulmschneider (1967, 1971) and Ulmschneider and Kalkofen (1978), we have calculated the dissipation rates of upward-travelling slow-mode acoustic shock waves in umbral chromospheres for two umbral chromosphere models, a plateau model by Avrett (1981) and a gradient model by Yun and Beebe (1984). The computed shock dissipation rates are compared with the radiative cooling rate given by Avrett (1981). The results show that the slow-mode acoustic shock waves with a period of about 20 second can heat the low umbral chromospheres travelling with a mechanical energy flux of $2.6{ imes}10^6;erg/cm^2s$ at a height of $300{sim}400km$ above the temperature minimum region.