A standstill seal configured to form a seal with a rotatable shaft so as to prevent leakage of a process fluid past the standstill seal when the shaft is not rotating, the standstill seal comprising: a flexible band surrounding the shaft, the flexible band comprising a relatively thicker central region from which relatively thinner side regions extend longitudinally in the direction of sealing of the central region with the shaft, or with an intermediate structure that is sealed to the shaft, when seen in an axial cross-sectional view, the central region being substantially rectangular in longitudinal cross section; a housing configured to house the flexible band; a pair of cover plates underlying the side regions of the flexible band and configured to prevent the side regions from being deflected past the cover plates, a gap being provided between the cover plates through which the central region of the flexible band can be extended; a control fluid inlet configured to provide fluid communication between a source of pressurized control fluid and a rear surface of the flexible band; and a controller; the standstill seal being configured, when the controller applies the pressurized control fluid to the control fluid inlet, to press the rear surface of the flexible band toward the gap, thereby extending the central region of the flexible band through the gap, such that it makes contact and forms a seal with the shaft, or with the intermediate structure that is sealed to the shaft, whereby flexibility of the flexible band is provided by the side regions; the standstill seal being configured, when the controller ceases to apply the pressurized control fluid to the control fluid inlet, to withdraw the central region of the flexible band away from the shaft or intermediate structure. a flexible band surrounding the shaft, the flexible band comprising a relatively thicker central region from which relatively thinner side regions extend longitudinally in the direction of sealing of the central region with the shaft, or with an intermediate structure that is sealed to the shaft, when seen in an axial cross-sectional view, the central region being substantially rectangular in longitudinal cross section; a housing configured to house the flexible band; a pair of cover plates underlying the side regions of the flexible band and configured to prevent the side regions from being deflected past the cover plates, a gap being provided between the cover plates through which the central region of the flexible band can be extended; a control fluid inlet configured to provide fluid communication between a source of pressurized control fluid and a rear surface of the flexible band; and a controller; the standstill seal being configured, when the controller applies the pressurized control fluid to the control fluid inlet, to press the rear surface of the flexible band toward the gap, thereby extending the central region of the flexible band through the gap, such that it makes contact and forms a seal with the shaft, or with the intermediate structure that is sealed to the shaft, whereby flexibility of the flexible band is provided by the side regions; the standstill seal being configured, when the controller ceases to apply the pressurized control fluid to the control fluid inlet, to withdraw the central region of the flexible band away from the shaft or intermediate structure.