Elling was born in 1858 in what is now Oslo. He studied piano and composition in Leipzig from 1877–78 and in Berlin from 1886–87. From 1896–1908, he was teacher at musikkonservatoriet i Oslo. He was also (1908–26) organist at Gamlebyen kirke.
As a composer, he wrote symphonies, a violin concerto, chamber music, an opera, and more than 200 songs, most in the 1890-1905 period. His works are seldom performed now, but many musicians were influenced by him, such as Fartein Valen, who studied music under Elling.
Elling was named to a state stipend in 1899, and continued a folk music led collection across many parts of the country: Trøndelag, the valleys of Oppland, Telemark and Setesdal. At the same time, folk music collector Olav Sande was also named to a state stipend, and the two "divided the country between them", Sande taking the music tradition from Sogn to Vest-Agder. Elling's mandate was to collect music and also work to preserve it. He published a range of music books with titles such as Norske folkemelodier for klaver, Norske folkeviser for sang og klaver and Slåtter for fiolin og klaver. Both at the time, and since, he has been criticised for wanting to rearrange folk music to fit with classical music's style.
He was the brother of engineer Ægidius Elling, who invented the gas turbine.
- Symphony in A major (1890)
- Kosakkerne, Opera (1894)
- Den forlorne Søn, Oratorio (1896)
- String Quartet in D major
- Violin Concerto in D minor
- Norske komponister ved Musikkfesten i Bergen, 1898, Document.dk, Retrieved 22 May 2016
- Bjørn Aksdal. "Catharinus Elling" in: Norsk biografisk leksikon, 2. utg.
- Norges musikkhistorie, bd 3. 1999