A prosthetic heart valve includes a frame that is radially collapsible and expandable between a collapsed configuration and an expanded configuration, and defines a longitudinal axis. A leaflet structure situated within the frame, and a sealing member is disposed around the frame. The sealing member can include a first portion extending circumferentially around a portion of the frame, the first portion being configured to resiliently stretch in a direction along the longitudinal axis between a first state corresponding to the expanded configuration of the frame and a second state corresponding to the collapsed configuration of the frame. The sealing member can include a second portion extending circumferentially around a portion of the frame, the second portion being configured to resiliently stretch in a circumferential direction between a first state corresponding to the collapsed configuration of the frame and a second state corresponding to the expanded configuration of the frame.