Pregnant women and children sometimes need to undergo chest CT scans during the COVID-19 pandemic. This study estimates fetal and pediatric doses from chest CT scans. Organ doses and effective doses were calculated using the VirtualDose-CT software. Two groups of computational human phantoms, pregnant females at three gestational stages (3, 6 and 9 months) and pediatric patients at four different ages (the newborn, 1-, 5-, and 10-year-old) were used in this study. The results of doses normalized to CTDIvol can be used universally for other dosimetry studies. Based on our calculations and international survey data of CTDIvol, fetal absorbed doses for chest CT were found to be 0.04-0.36, 0.05-0.44, 0.07-0.61 mGy, for 3, 6 and 9 months of pregnancy, respectively. When the scan range is extended to the abdominal region, total fetal doses increase by 3.9-fold. The effective doses from chest scans were 1.62-13.77, 1.58-13.46, 1.57-13.33, 1.29-10.98 mSv, for the newborn, 1-, 5-, and 10-year-old children, respectively. In addition, the effects of specific axial scan ranges exceeding the thorax region are evaluated. Although organ doses from chest CT scans are small, such data allow radiologists and patients to be informed of the dose levels as well as ways to avoid unnecessary radiation.