If finch eggs do not hatch after three weeks, the eggs may be infertile or may not have been incubated properly.
Infertility: Eggs can be infertile if the male was not fertile, fertilization failed, or eggs were damaged during laying.
Incubation: Finch eggs require constant temperature and humidity. Ideal conditions are about 99–102°F and 55–65% humidity. Eggs that are too cold, hot, or dry will not hatch.
Troubleshooting: Check the male's fertility, the condition of the eggs, and the incubation temperature and humidity. If problems persist, consult a veterinarian or experienced bird breeder.