At the end of World War II, Mednis's family moved to the US. He was trained as a chemical engineer, then worked as a stockbroker, but became best known as a chess author. Mednis wrote 26 chess books, including Practical Rook Endings (1982), and hundreds of chess articles. He and Robert Byrne annotated many games for Chess Informant.
Mednis finished second in the 1955 World Junior Championship behind Boris Spassky (the two drew their game). He was the first player to beat Bobby Fischer in a US Championship. He played on the 1962 United States Olympiad team and finished equal third in the 1961-62 US Championship. Tournament results included third at Houston 1974, equal fourth at New York 1980, and equal first at Puerto Rico 1984. The Puerto Rico Chess Federation, rather than the United States Chess Federation, formally proposed him for the Grandmaster title. He played in the 1979 Interzonal tournament in Riga, his birthplace.
Mednis suffered a fatal heart attack in 2002 in Woodside, Queens, New York.