1. A study was conducted on ~14000 ostrich eggs to estimate genetic parameters for eggshell traits that could benefit the hatchability of ostrich eggs. Traits measured included the number of pores on the eggshell, the average diameter of these pores, the total area of pores on the eggshell, permeability (pore area/shell thickness) and eggshell thickness. 2. Heritability estimates ranged from 0·16 for total pore area to 0·41 for the natural logarithm of pore count. The heritability estimates for water loss on 21 and 35 d (WL21 and WL35) of incubation were high at 0·23 and 0·24, respectively. 3. On a genetic level, pore count was negatively correlated with average pore diameter (-0·73) and shell thickness (-0·28), whereas it was positively correlated with total pore area (0·58), WL21 (0·24) and WL35 (0·34). The direct and maternal genetic correlations of pore count with total pore area (0·58) and permeability (0·59) were high and significant. Permeability was positively correlated to WL21 and WL35, both on the direct and maternal genetic levels. 4. The estimated genetic parameters indicate that it should be possible to select for the various eggshell traits in ostrich eggs, or for permeability and water loss. However, as a trait with an intermediate optimum, direct selection for permeability and other eggshell traits would not be straightforward, and the possible application of these results to improve hatchability of ostrich eggs in the future needs consideration.