The UV5R MK4 is the most common body type available. There are models with varying internal components such as the BF-F8 HP that share the same body. If your radio body looks like this, the UV5R Exoskeleton is compatible.
The UV-5RE and UV-5R plus models are also compatible with the UV5R Exoskeleton.
The new 2021 Baofeng UV5R MK5 from Mirkit Is compatible with the UV5R Exoskeleton. Due to slight body geometry changes, the clearance around the volume knob is very tight. The Exoskeleton does make contact with the top of the radio on the button side, but it is still fully functional.
The UV82 Exoskeleton fits all radios that have the body style pictured directly above. Shown here is a Baofeng UV82 HP, the most common radio of this body style. It is compatible with the UV82 Exoskeleton.
This example is a Btech MURS-V1. It has the same body style as other UV82 radios and therefore its compatible.
The new Baofeng UV82 MK5 MP offering from Mirkit is also compatible as the body style hasn't changed. If your radio body looks like this, the UV82 Exoskeleton is compatible.