As the computer system has developed much in this highly information-oriented society, database security has become a very important problem and its backup strategies need to be made more efficiently and safety. The image copy method has been used as the most simple and dependable recovery mechanism for media failure. However, this method spends high overhead costs for massive data transmission and much processing time in the normal operation of the database. To cover such weak points, incremental and full backup methods are adopted before updated trucks reach a predetermined level. Moreover, when the number of full backup files exceeded a predetermined level, we stop incremental and full backups and switch it to the image copy. This paper applies cumulative damage model to backup of files in a database system, by putting damage shock by update, failure shock by database failure and damage by dumped files, and considers the tradeoff among overhead costs of image copy and incremental, full backup methods, and discusses analytically an optimal policy for the image copy backup interval. Finally, numerical examples are given in the case of Poisson process and exponential distributions.