"Beauty Knows No Pain" was never performed or recorded by itself. Instead it was embedded in a sequence of songs that opens with "Society Pages" and "I'm a Beautiful Guy," and continues with "Charlie's Enormous Mouth," "Any Downers?," and "Conehead." This suite (so to speak -- it lacks thematic unity to really form a single composition) was performed in its entirety in 1980 and released following the same order of appearance on the 1981 studio album You Are What You Is, comprising the whole of side two of the original two-LP set. Later performances in 1981 omitted the last two tracks.
Like the previous tracks in the sequence, "Beauty Knows No Pain" takes its cue from the last line of the previous song and provides in its own last verse the starting point for the next piece. The vain lifestyle and subtlety lacking seduction technique of the "Beautiful Guy" prompt a reflection on women and men who value "beauty" (seen as a form of social acceptance) above comfort. Bikini wax, nail polish, makeup, and "a pair of shoes that makes you wanna die" are all part of the burden people who are oblivious to the fact that "Beauty is a lie" must endure. The last verse of the song hardly fits with what came before it -- it is another attempt to create a link to the next piece.
From a musical standpoint, "Beauty Knows No Pain" is the most complex number of the sequence. It features odd (and changing) time signatures, lots of overdubs, and crazy arrangements. The last part of the piece reverses to a swing motif, tying it even more closely to "It's a Beautiful Guy." Early live versions were simpler, but in the studio Zappa added a lot of flesh to the bone. Consequently, subsequent performances (such as the one documented on You Can't Do That on Stage Anymore, Vol. 3) are not as satisfying as the album version, even though the band's effort to reproduce every detail was praiseworthy.