A cold storage evaporator including a core including a plurality of refrigerant tubes in which refrigerant flows, a plurality of fins through which external air passes, and a plurality of cold storage containers containing cold storage material, the refrigerant tubes, the fins, and the cold storage containers being stacked, the cold storage evaporator comprising: a plurality of heat exchange units (U1, U2, U3,...), each heat exchange unit (U1, U2, U3,...) including one of the fins, one of the refrigerant tubes, one of the cold storage containers, and another one of the refrigerant tubes that are stacked in order in a direction crossing a direction in which the external air passes, herein after called the stacking direction wherein the heat exchange units (U1, U2, U3,...) are arranged in the stacking direction, the cold storage container includes a first plate defining a first side of the cold storage container in the stacking direction and a second plate defining a second side, opposite to the first side, of the cold storage container in the stacking direction, the first plate and the second plate define therebetween a cold storage material space for containing cold storage material, the first plate has a first joint plate portion surrounding an entire periphery of the first plate, the second plate has a second joint plate portion surrounding an entire periphery of the second plate and joined to the first joint plate portion, the first plate has an inner portion that is inside the first joint plate portion and that is a first bulging portion bulging toward the first side, the first bulging portion has a plurality of first recessed portions that are recessed inward toward the inside of the cold storage container, that is in the stacking direction, the second plate has an inner portion that is inside the second joint plate portion is a second bulging portion bulging toward the second side, the second bulging portion has a plurality of second recessed portions that are recessed inward toward the inside of the cold storage container, that is in the stacking direction, a dimension of each cold storage container in the stacking direction is smaller than a dimension of each fin in the stacking direction, an endmost surface of the first bulging portion and an endmost surface of the second bulging portion in the cold storage container are bonded to the refrigerant tubes to allow outer surfaces of the refrigerant tubes to close the first recessed portion and the second recessed portion, characterized in that A/B is 0.45 or greater and 0.75 or smaller, and A is 2.5 mm or greater and 4.5 mm or smaller, where A represents the dimension of each cold storage container in the stacking direction, and B represents the dimension of each fin in the stacking direction, wherein C is 1.5 mm or greater and 2.5 mm or smaller, and B/C is 2.0 or greater and 4.5 or smaller, where C represents a dimension of each refrigerant tube in the stacking direction a plurality of heat exchange units (U1, U2, U3,...), each heat exchange unit (U1, U2, U3,...) including one of the fins, one of the refrigerant tubes, one of the cold storage containers, and another one of the refrigerant tubes that are stacked in order in a direction crossing a direction in which the external air passes, herein after called the stacking direction wherein the heat exchange units (U1, U2, U3,...) are arranged in the stacking direction, the cold storage container includes a first plate defining a first side of the cold storage container in the stacking direction and a second plate defining a second side, opposite to the first side, of the cold storage container in the stacking direction, the first plate and the second plate define therebetween a cold storage material space for containing cold storage material, the first plate has a first joint plate portion surrounding an entire periphery of the first plate, the second plate has a second joint plate portion surrounding an entire periphery of the second plate and joined to the first joint plate portion, the first plate has an inner portion that is inside the first joint plate portion and that is a first bulging portion bulging toward the first side, the first bulging portion has a plurality of first recessed portions that are recessed inward toward the inside of the cold storage container, that is in the stacking direction, the second plate has an inner portion that is inside the second joint plate portion is a second bulging portion bulging toward the second side, the second bulging portion has a plurality of second recessed portions that are recessed inward toward the inside of the cold storage container, that is in the stacking direction, a dimension of each cold storage container in the stacking direction is smaller than a dimension of each fin in the stacking direction, an endmost surface of the first bulging portion and an endmost surface of the second bulging portion in the cold storage container are bonded to the refrigerant tubes to allow outer surfaces of the refrigerant tubes to close the first recessed portion and the second recessed portion, characterized in that A/B is 0.45 or greater and 0.75 or smaller, and A is 2.5 mm or greater and 4.5 mm or smaller, where A represents the dimension of each cold storage container in the stacking direction, and B represents the dimension of each fin in the stacking direction, wherein C is 1.5 mm or greater and 2.5 mm or smaller, and B/C is 2.0 or greater and 4.5 or smaller, where C represents a dimension of each refrigerant tube in the stacking direction