A cardiac constraint jacket is formed of flexible material defining a volume between an open upper end and a lower end. The jacket is dimensioned for an apex of a patient's heart to be inserted into the volume through the open upper end and for the jacket to be slipped over the heart. A delivery device is used to place the jacket on the heart. The delivery device includes a plurality of attachment locations. Each of the attachment locations is releasably secured to separate positions surrounding a periphery of the open upper end of the jacket. The delivery device also includes a control arrangement which is selectively movable between an open position and a closed position. The control arrangement is connected to the attachment locations such that the attachment locations are in a compact array urging the open upper end of the jacket into a collapsed configuration when the control member is in the closed position. When the control arrangement is in the open position, the attachment locations are in an open array. The attachment locations urge the open upper end of the jacket into an open configuration sufficient for the heart to be inserted into the jacket volume through the open upper end and for the jacket to be slipped over said heart.