Henry Elling was born in Germany on December 9, 1842. After the death of his parents when he was about 15, he emigrated to the United States with a younger brother. The two boys settled in Missouri to live with an older brother. While learning English, Henry supported himself working as a farm laborer. He then secured work in a mercantile business. In 1861 he moved to Levenworth, Kansas, and then followed the Colorado gold rush to Denver in 1862. He earned enough there as a clerk in a clothing business to purchase a stock of goods which he hauled by ox team to Virginia City, Montana Territory. He opened a store in October 1864. The following year he moved to Helena where he started another store and also dealt in gold dust. At first he did very well, but prices dropped and his business failed. He moved back to the Midwest to try to recoup his losses.

After several years in the Midwest, Elling returned to Virginia City, Montana. He at first opened a mercantile business, but after 1873 was predominantly a banker. He established the Banking House of Henry Elling, a private bank. His business was based on his personal evaluation of his customers and his extensive knowledge of gold dust. Many considered his loans rash, but his instincts usually served him well. He also helped organize banks in a number of other communities, including the Carbon County Bank in Red Lodge, the State National Bank of Miles City, the Bank of Fergus County, and the Union Bank and Trust Company of Helena. In 1899 Elling reorganized his Virginia City bank as the Elling State Bank. This bank continued to operate after Elling's death. under the management of S.R. Buford, Mary B. Elling, and Karl Elling.

In addition to his banking business, Elling maintaining his mercantile interests through partnerships with others. He was the "and Company" of S.R. Buford and Company. He was also a partner in the Elling and Buford ranch; the Elling and Hyndman flour mill; the Elling, Morris and Word quartz mill; the Elling, Hickman and Olds mining claim; the Elling, Knight and Buford hardware business; and others. In 1872 Elling became a partner in Ramsey, French and Company to build and operate the Silver Spring Grist Mill. The mill later was operated by a series of lessees.

Elling became one of the largest landowners in Madison County. An abstract of his property ownership covers 80 pages of a register. Included were extensive ranch and farm lands, mining claims, and city lots and buildings.

Fraternally, Henry Elling was a member of the Masons, the Knights Templar, the Ancient Order of United Workmen, and the Elks. Politically he was a Republican, but unlike his activist Democratic partner S.R. Buford, Elling refused to become involved in politics.

Henry Elling married Mary B. Cooley, daughter of W.A. Cooley, in 1870. The couple had ten children, seven of whom survived Elling. Henry Elling died of pneumonia on November 14, 1900, after an illness of only four days.