A heady mix of slacker melody, distortion, lo-fi production and noise, the most obvious band reference to make with relation to A Grave With No Name is Animal Collective, who - despite having a much cleaner sound overall - are well-known for their chanting hedonistic noise.
A Grave With No Name's music, however, sounds more like its aiming towards band member Panda Bear's solo stuff; this is, attempting to push swelling vocals over and above experimental fuzz.
It is difficult to tell how much of A Grave With No Name's thick and hazy sound is deliberate, and how much is simply because most of their tracks were recorded in a bedroom. If the latter, then the harmonies might benefit from being freed up from their slightly swampy surroundings.