The opening has an ominous feel to it and a cough is audible during the song's middle eight. It was originally credited to just Brian Wilson. Mike Love's name was added as a result of a lawsuit filed by him against Wilson in the 1990s.
The opening chords are whole notes played on electric guitar and bass. The song begins with a minor i chord in the key of D minor, moves to a major IV, comes back to the minor i, and then moves to a major VI chord, a IV in the key of F. The song then modulates to the key of F major (the relative major of D minor) through a substituted plagal cadence, using a I-ii progression to solidify the new tonic of F.
The verse begins with another I-IV-I progression, ending on an IV chord in the first line. The second line begins the same as the first, but moves to a major ♭VII (in D minor the neapolitan chord), and then modulates to the relative minor through use of a iii chord (A minor, the V in the key of D minor), the A minor moving to a D minor via an authentic cadence. The chorus/bridge ("I never thought a guy could cry") uses the same chord progression found in the introduction (D: i-iv-i-VI(IV in F), coming back to the key of F for the final line. This repeats for the second verse, before going into the organ solo.
After the second chorus, the song modulates again from F to D minor, this time through the usage of the ♭VII (E♭ major), which is a tritone substitution for the V of D. The solo follows the same general progression of the introduction and chorus. Another run of the verse/chorus follows, and the song then fades out with repeated I-IV cadences.
"Wendy" peaked at No. 44 on the Billboard Hot 100, at No. 36 in Germany and at No. 5 in Switzerland in July 1967 when it was nominally the B-side of "Good Vibrations" — as it was everywhere outside the US.