Alnæs was born in Fredrikstad, as the son of headmaster Johannes Jørgen Lauritz Alnæs (1835–1916) and Elise Martine Hansen (1851–1931). He married Emilie Thorne (1882–1976) in 1903. He was the father of author Lise Børsum, and grandfather of novelist Finn Alnæs and artist Bente Børsum.
In 1888 he was enrolled at the Music and Organist School in Oslo (Musikkonservatoriet i Oslo). Alnæs studied piano with Westye Waaler, organ with Peter Brynie Lindeman as well as harmonics, counterpoint and composition with Iver Holter. In April 1892, after Alnæs had finished his studies in Oslo, he studied in Leipzig with Carl Reinecke and, after the première of his first symphony in 1896, in Berlin with Julius Ruthardt.
For many year, he played the organ in several churches and conducted choirs. During the years 1895-1907 he was organist at Bragernes Church in Drammen. From 1907-16 he was at Uranienborg Church in Oslo and between 1916-32 at Oslo Cathedral. He helped found the Norwegian Composer's 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). 
A number of songs by Alnæs have been recorded by the likes of Kirsten Flagstad and Feodor Chaliapin. In 2007 the first recording of Alnæs's Piano Concerto in D major, Op. 27 (published c. 1919) was released; it featured Piers Lane as the piano soloist and the Bergen Philharmonic Orchestra conducted by Andrew Litton. In early 2010 the premiere recording of his two symphonies - no.1 in C minor, Op.7 and no.2 in D major, Op.43 - was released, with the Latvian National Symphony Orchestra conducted by Terje Mikkelsen.
- "Eyvind Alnæs". Den Store Danske. Retrieved March 1, 2018.
- Grinde, Kirsti. "Eyvind Alnæs". In Helle, Knut. Norsk biografisk leksikon (in Norwegian). Oslo: Kunnskapsforlaget. Retrieved 11 December 2014.
- "Eyvind Alnæs (1872–1932)". lokalhistoriewiki.no. Retrieved March 1, 2018.
- Trond Olav Svendsen. "Norsk Komponistforening". Store norske leksikon. Retrieved March 1, 2018.
- see Hofmeisters Monatsbericht, 1919, p.78
- "Alnæs, Eyvind: Symphony No. 1, Symphony No. 2". Sterling CD. January 2010. Retrieved Dec 31, 2010.
- "Kongens fortjenstmedalje". lokalhistoriewiki.no. Retrieved March 1, 2018.
- Eyvind Alnæs at Find a Grave
- Brief biography from Norwegian Melodies
- Free scores by Eyvind Alnæs at the International Music Score Library Project (IMSLP)
- Free scores by Eyvind Alnæs in the Choral Public Domain Library (ChoralWiki)
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