A coin wrapping machine includes a discrimination unit which detects images of the front face and rear face of coins during conveyance, and which discriminates the coins, a sorting unit which sorts the coins to one of a first side and a second side based on the discrimination results of the discrimination unit, a stacking unit which stacks the coins sorted to the first side by this sorting unit into columnar form with a prescribed number of coins, a wrapping unit which wraps stack of coins in columnar form, and a controller which controls the sorting unit based on the discrimination results so that at least one of an outside face of a coin at one end of the stack of coins and a second outside face of a coin at the other end of the stack of coins is the rear face.