The purpose of this article is to inform and possibly help you understand and fix the problem.
The Fluke-87 has a feature called input alert and the reason for this function is to keep you from blowing the fuses and potentially damage the meter. If you have a test lead plugged into one of the current input jacks and the other lead plugged into the common jack and try to measure voltage you will blow the fuse and potentially damage the meter.
The way the input alert function works is it can sense if the test leads are plugged into either the A input or the mA/uA input but it can also detect if dust, water, metal fragments or anything conductive and still alert you. Even if the humidity is too high you can have condensation inside the meter and it will trigger the input alert function.
The potential solution is to use forced air and blow out the input jacks to see if you can dislodge the fragments or disperse the water. If the meter was dropped into water or water poured over it the evaporation can take a long time before it will evaporate and or water could have contaminates and be conductive to cause the input alert to still be active. You would have to open the meter and lay the two halves of the meter under a lamp to help decrease the evaporation time. If you suspect the water has conductive items such as salt water you may have to clean it with distilled water.
Once you have completed the steps above the meter should stop beeping when you turn it on, if not you should contact the Fluke service center (888-993-5853 or firstname.lastname@example.org).