Protection against blast and ballistic damage is improved by encapsulating or sandwiching rigid inclusions (for example, tiles) or a rigid plate by a high-strain rate hardening elastomer. Typical high-strain rate hardening elastomers include polyurea and polyurethane. If desired, the inclusion or plate may be wrapped in a cloth and/or fabric before encapsulation/sandwiching. The armor may be used independently of a substrate or may be attached by any means to a substrate that it is intended to protect.