Elias Brown attended the public schools of his home and then embarked on a political career. First, he was a member of the Democratic- Republican Party. In 1820 he was one of the electors in the re- election of President James Monroe. In 1828 he acted as one of the electors of President John Quincy Adams, who lost in this election against Andrew Jackson. Around the same time, Brown needs to Jackson and his then newly founded Democratic Party to be converted.
In the congressional elections of 1828, Brown was in the fifth electoral district of Maryland in the U.S. House of Representatives in Washington DC chosen, where he took up his new mandate on March 4, 1829. Until March 3, 1831, he was able to complete a term in Congress. After the inauguration of President Jackson in 1829, was discussed inside and outside of Congress vehemently about its policy. It was about the controversial enforcement of the Indian Removal Act, the conflict with the State of South Carolina, which culminated in the Nullifikationskrise, and banking policy of the President.
After the end of his time in the U.S. House of Representatives sat Brown continued his political career at the state level. In the years 1834 and 1835, he sat in the House of Maryland; 1836 to 1838 he was a member of the State Senate. During this time he must have again changed his party affiliation, because in the presidential election of 1836 he was an elector of William Henry Harrison, who was a candidate for the Whig party. In the same year, Brown was a delegate to a meeting on the revision of the Constitution of Maryland. After that, he is no longer politically have appeared. He died on July 7, 1857 near Baltimore.