Šoškić is a surname. Notable people with the surname include:
Branislav Šoškić (born 1922), President of the Socialist Republic of Montenegro 1985–1986
Budislav Šoškić (1925–1979), President of the People's Assembly of the Socialist Republic of Montenegro
Milutin Šoškić (born 1937), Serbian former goalkeeper who is one of FK Partizan's biggest legends
Dejan Šoškić, Serbian economist