A report presents the concept of Flexshield a class of versatile, lightweight, flexible shields for protecting spacecraft against impacts by small meteors and orbiting debris. The Flexshield concept incorporates elements of, but goes beyond, prior spacecraft-shielding concepts, including those of Whipple shields and, more recently, multi-shock shields and multi-shock blankets. A shield of the Flexshield type includes multiple outer layers (called bumpers in the art) made, variously, of advanced ceramic and/or polymeric fibers spaced apart from each other by a lightweight foam. As in prior such shields, the bumpers serve to shock an impinging hypervelocity particle, causing it to disintegrate vaporize, and spread out over a larger area so that it can be stopped by an innermost layer (back sheet). The flexibility of the fabric layers and compressibility of the foam make it possible to compress and fold the shield for transport, then deploy the shield for use. The shield can be attached to a spacecraft by use of snaps, hook-and-pile patches, or other devices. The shield can also contain multilayer insulation material, so that it provides some thermal protection in addition to mechanical protection.