There have been many instrumental versions of this song, most entitled Lachrimae (or Lachrymae, literally "tears"). In this case the instrumental version was written first, as Lachrimae pavane in 1596, and lyrics were later added. It is believed that the text was written specifically for the music, and may have been written by Dowland himself. Lachrimae exists in over 100 manuscripts and printings in different arrangements for ensemble and solo. The Lachrimaes tend to be much more abstract than other music based on dance forms of the time, and do not completely follow the structure of the standard pavan in terms of length of phrases; they are also more contrapuntal.

Instrumental versions by Dowland include Lachrimae for lute, Galliard to Lachrimae for lute and Lachrimae antiquae (1604) for consort. Dowland also published Lachrimae, or Seaven Teares (London, 1604), a collection of consort music which included a cycle of seven Lachrimae pavans based on the falling tear motif. Thomas Morley set the "Lachrimae Pauin" for the six instruments of a "broken consort" in his First Booke of Consort Lessons (London, 1599).

Other composers have written pieces based on the work, including Jan Pieterszoon Sweelinck and Thomas Tomkins, while John Danyel's Eyes, look no more pays clear homage to the piece, as does John Bennet's Weep, O Mine Eyes. In the 20th century, American composer and conductor Victoria Bond wrote "Old New Borrowed Blues (Variations on Flow my Tears)". Benjamin Britten quotes the incipit of Flow My Tears in his Lachrymae for Viola, a set of variations on Dowland's ayre If My Complaints Could Passions Move. In 2006, the British electronic music group Banco de Gaia produced a vocoded version called "Flow my Dreams, the Android Wept".

Lachrimae became one of the favorite improvisational themes of the 16th and 17th century. As they have not been preserved in written form, nearly all versions have been consigned to oblivion.