Evaporator having cold thermal energy storage function

An evaporator with a cool storage function, comprising:

• a plurality of refrigerant flow tubes each having a first side wall and a second side wall opposite to the first side wall and provided to form spaces between the first side wall and the second side wall such that the first side wall of one of the plurality of refrigerant flow tubes faces the second side wall of another of the plurality of refrigerant flow tubes, the spaces having a first part and a second part other than the first part;
• fins provided in the first part of the spaces;
• cool storage material containers containing a cool storage material, each of the cool storage material containers having a longitudinal direction and including a third side wall and a fourth side wall opposite to the third side wall, the third side wall and the fourth side wall having first convex portions and second convex portions, respectively, the cool storage material containers being provided in the second part of the spaces such that the first convex portions contact the first side wall of the one of the plurality of refrigerant flow tubes and the second convex portions contact the second side wall of the another of the plurality of refrigerant flow tubes, the first convex portions and the second convex portions extending to incline with respect to the longitudinal direction, wherein the interiors of all of the cool storage material containers are connected with one another via a communication member.