Abstract: A standstill seal prevents leakage of a process fluid when a shaft is not rotating. The seal includes a flexible band surrounding the shaft that includes a thick, substantially rectangular center region from which thinner side regions extend. Application of pressurized control fluid to a rear surface of the band causes the central region to extend through a gap between cover plates to form a seal with the shaft or an intermediate structure. Depressurizing of the control fluid causes the central region to be withdrawn from the shaft, either entirely due to elasticity of the band, or with the assistance of springs. In various embodiments, the seal is formed radially inward or axially. The side regions can be substantially flat or curved. The standstill seal can be unitary with a rotating shaft seal, and can be upstream or downstream thereof. The control fluid can be the process fluid.