Coudrey was elected a member of the municipal house of delegates of St. Louis in 1897 and served for two years. He became interested in various business enterprises in St. Louis. Coudrey was at one time president of the Twenty-eight Ward Republican League Club. He successfully contested as a
Republican the election of Democrat
Ernest E. Wood to the Fifty-ninth Congress. During the election, there was gross fraud and Coudrey was not seated until almost the end of the Congress' first session. He was reelected to the Sixtieth and Sixty-first Congresses and served from June 23, 1906, to March 4, 1911. He was not a candidate for renomination in 1910 to the Sixty-second Congress. He moved to
New York City in 1911. He engaged in the real estate, insurance, and publishing businesses. ==Later life and death==