An APC UPS(Uninterruptible Power Supply) battery backup is designed to let you know when the device is running off battery power or not performing correctly using a series of beeping sounds. In order to stop the device from beeping constantly, you need to set the voltage dip switches and test the internal batteries. There may also be a problem with the way that your home's electricity is performing as well that needs to be addressed. Once you have troubleshooted the battery backup, you can prevent it from constantly making the beeping sounds.
Test the UPS device to make sure that the internal battery is working correctly. Plug the unit into a power outlet on your wall and let it charge for the amount of time suggested in your owner's manual. Plug your computer monitor into one of the jacks labeled "Battery + Surge Protection", then remove the battery backup's AC cable from the power outlet. If the monitor stays powered on, the battery is not defective and you can eliminate that possibility from the list of problems causing the beeping.
Use the battery backup's dip switches to determine when the unit will revert into battery mode which cause the beeps. Each model APC battery backup may use a different configuration of dip switch settings to adjust the voltage settings so refer to the manual for each switch's purpose. Pushing dip switch "2" upward to set the voltage indicator to 98 volts rms whereas when "3" is pushed upward, it will be set to 93 volts rms. Setting both "2" and "3" upward will tell the device to change to battery when its voltage drops to 88 volts rms whereas when switches "2" and '3" are both set downward, the device will change to battery mode when voltage drops under 103 volts rms. If you have to set both switches to their downward positions then you are most likely experiencing a problem with the power in your home which is making the battery backup use the internal battery and causing the repetitive beeping.
Call your local electrical company and notify them that you believe there is an issue with the voltage distribution within your home then set up an appointment to have the problem looked at. They will come and check with a voltmeter to see if the voltages being output to your home's outlets are adequate.