Alnæs studied piano with Westye Waaler, organ with Peter Brynie Lindeman as well as harmony, counterpoint and composition with Iver Holter.

He helped found the Norwegian Composers' Union (Norsk Komponistforening) in 1917 and served as chairman from 1921-23.

Alnæs wrote music in a late Romantic style; his output included two symphonies, one set of symphonic variations, a piano concerto, pieces for piano, chorale preludes for organ, choral works, and art songs (in Norwegian, romanser).

[4] Alnæs received the King's Medal of Merit (Kongens fortjenstmedalje) in gold in 1922, and in 1932 was appointed a Knight 1st Class in the Order of St. Olav.

27 (published c. 1919)[6] was released; it featured Piers Lane as the piano soloist and the Bergen Philharmonic Orchestra conducted by Andrew Litton.