A lens module in a head-mounted device may include a fluid-filled chamber, a semi-rigid lens element that at least partially defines the fluid-filled chamber, and at least one actuator configured to selectively bend the semi-rigid lens element. The semi-rigid lens element may become rigid along a first axis when the lens element is curved along a second axis perpendicular to the first axis. Six actuators that are evenly distributed around the periphery of the semi-rigid lens element may be used to control the curvature of the semi-rigid lens element. The semi-rigid lens element may initially be planar or non-planar. For example, the semi-rigid lens element may initially have a spherically convex surface and a spherically concave surface. A tunable spherical lens may be incorporated into the lens module to offset a parasitic spherical lens power from the semi-rigid lens element.