Critical insulation thickness is known to refer to the insulation thickness that maximises the rate of heat transfer in cylindrical and spherical systems. The same analogy is extended to the rate of entropy generation in the present study. The possible critical insulation thickness that yields a maximum rate of entropy generation is investigated. Entropy generation is related to heat transfer through and temperature distribution within the insulation material. It is found that there exists a critical insulation thickness for maximising the rate of entropy generation that is a function of the Bi number and the surface to ambient temperature ratio. The solution of such critical thickness is formulated analytically for both cylindrical and spherical geometries. It is also found that the critical insulation thickness for the rate of entropy generation does not coincide with that for the rate of heat transfer.