PROBLEM TO BE SOLVED: To provide an evaporator with a cold storage function capable of further reducing manufacturing costs.SOLUTION: A cold storage material container 15 of an evaporator with a cold storage material function, is composed of two sheets of aluminum plates 29, 31 joined to each other. The cold storage material container 15 is provided with a cold storage material enclosing portion 15a formed by expanding both aluminum plates 29, 31 outward. Only a lower end portion of the first aluminum plate 29 as one of two sheets of aluminum plates 29, 31 constituting the cold storage material container 15 is projected downward with respect to a lower end portion of the other second aluminum plate 31. The lower projecting portion 32 is positioned between both refrigerant circulation pipes of the cold storage material case 15. On the lower projecting portion 32 of the first aluminum plate 29, a plurality of air-passing suppressing portions 33, 34 composed of projections, the longitudinal direction of which is
