Angst is the surname of:
Fritz Angst (1944–1976), German-language Swiss author better known as Fritz Zorn
Heinrich Angst (1915–1989), Swiss bobsledder
Jules Angst (1926–2026), Swiss psychiatrist and academic
Max Angst (1921–2002), Swiss bobsledder
Randy Angst, American politician, member of the Missouri House of Representatives from 2003 to 2004
Richard Angst (1905–1984), Swiss cinematographer