A concept for a miniature, solid‐state gas compressor is examined. The device operates by the phased activation of voltage‐driven, electrostrictive ceramic blocks along a compression channel wherein a confined elastomer provides a motion‐amplifying medium for peristaltically closing the compression channel. The device is also self‐valving. Model estimates based on the nonlinear electromechanical parameters for paraelectric BaTiO3suggest that a small (∼5×5×9‐cm3), lightweight (∼1‐kg) device would supply ∼0.3 cm3per cycle at a compression ratio of 25:1 employing modest electric fields (∼20 kV/cm). At 500 Hz this corresponds to 38 mW of ideal Joule–Thompson refrigeration at 4.2 K using He gas. The efficiency of the device is estimated to be ∼85% (not including the power supply). A three‐cell mechanical simulator of the concept was built and tested, and it was demonstrated that compression and self‐valving can be achieved by peristaltically extruding an elastomer against a gas channel. An electronic power supply to drive the electrostrictive ceramics was designed, and a three‐cell supply was built and tested which demonstrated that voltages up to 150 V could be switched at frequencies up to 10 kHz using small, inexpensive components. A critique of practical considerations is given, and it is concluded that the concept is feasible but additional research is required in elastomeric materials and in fabricating relatively large ceramic capacitors (∼2×2×1 cm3). Currently available electrostrictive actuators are inadequate.