Provided a computer program product, system, and method for rebuilding damaged areas of a volume table using a volume data set for managing data sets assigned data units in a volume in a storage. A determination is made of damaged areas in a volume table providing information on data sets allocated in the volume. The determined damaged areas are formatted to produce reformatted areas to make the volume table usable. A volume data set in the volume having information on data sets configured in the volume is processed to determine from the volume data set salvaged data sets comprising the data sets in the volume not indicated in the volume table. Data set information is rebuilt in the reformatted areas of the volume table for the salvaged data sets.