Fresh shellfish can be stored in the fridge in an open vessel. Maintain humidity by placing a damp cloth on top. Do not place shellfish in water as they may spoil. You can store shellfish that completely close their shells for up to seven days. These include cockles, butter clams, littlenecks, and oysters. However, mussels can only be stored for up to four days. You can store shellfish that do not close their shells completely for up to four days. These include razor clams, geoducks, softshell clams, and horse clams.