Bax composed the Elegiac Trio during April and May of 1915. It is scored for flute, viola and harp, the same combination of instruments Debussy used in his sonata of the same year. The similarities are coincidental, for it is unlikely that either composer knew the other's piece. Bax's Elegiac Trio was first performed on March 26, 1917, in London's Aeolian Hall, as part of a concert sponsored by the Oriana Madrigal Society. Albert Fransella played flute, Miriam Timothy played harp, and the composer H. Waldo Warner was the violist. (The same musicians had given the first performance in Britain of Debussy's sonata less than two months earlier.) The publishing house of J. & W. Chester issued the Elegiac Trio in 1920, by which time Bax's fame was increasing in musical circles.

The Elegiac Trio does not contain the darker elements we find in many of Bax's works. This is surprising, for it was composed not long after the tragic Easter Uprising in Ireland, an event that affected Bax deeply because some of his friends were executed in its aftermath. Although it is just as much a reaction to the Easter Uprising as the contemporaneous Irish Elegy and In Memoriam Pádraig Pearse, the Elegiac Trio responds not with grief but with a dream of an earlier, better world.

In two parts, the Elegiac Trio evokes Medieval and Renaissance bards and their music through the accompanimental pattern in the harp part. In the first section, the longer and more developed of the two, the flute and harp claim all the melodic material, sometimes playing together and sometimes separately. All the while, the harp provides harmonic background with arpeggios—except in the most transparent passage of the piece, where the flute and viola begin trills while the harpist plays harmonics and glissandi with the left hand and the theme with the right. The unusual exploration of timbre marks this episode more than the melodic material, which, along with the harp figures, evokes the ancient Celtic past.

The "elegiac" portion of the piece begins in the second part. The tempo drops drastically and viola and the harp join in sounding a noble, evocative melody as the flute lends decorative flourishes and trills over arpeggios in the left hand of the harp part. The ethereal atmosphere is similar to that of some of the composer's later symphonies.

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