The rate of entropy generation during the steady conduction through a solid slab is investigated analytically. The effects of thermal conductivity and internal heat generation/sink on the total rate of entropy generation are discussed. Cases of uniform, spatial variable and temperature dependent thermal conductivity are considered. In addition, the case of introducing internal heat source/sink is discussed. It is concluded that the total rate of entropy generation per heat transfer rate in steady heat conduction through solid material is a function of only the rate of heat transfer, regardless of the distribution and or dependence of the thermal conductivity. The total rate of entropy generation during conduction in solid material can be eliminated by introducing internal heat generation/sink. The total rate of entropy generation during the transient heat conduction decreases with time and approaches its minimum value as the steady conduction is reached. ©2011 Academic Journals.