A high-resolution flexible active skin with a matrix of 32x24 individually addressable tactile pixels on a 4 mm pitch is reported, based on shape memory polymer (SMP) actuators. The intrinsic multistable nature of SMPs, and their more than hundred-fold variation in stiffness over a narrow temperature range, enables dense arrays of actuators exhibiting simultaneously large strokes and high holding forces. The control challenge of addressing a very large number of soft actuators is solved by patterning an array of miniature stretchable heaters on a thin SMP membrane, so that one single pneumatic supply is sufficient to rapidly and selectively reconfigure any or all elements. The device consists of a 40 µm-thick SMP layer, on which 32x24 stretchable heaters are integrated, interconnected by a flexible PCB and bonded to a stretchable 3D-printed pneumatic chamber. Each taxel can be individually controlled via row/column addressing, and requires 2.5 s to latch to a different state. The active skin weighs only 55 g and is 2 mm thick. More than 99% of the 768 taxels are fully functional, with a lifetime in excess of 20’000 cycles. This architecture enables applications in haptic displays, active camouflage, biomimetic robots, microfluidics, and new human machine interfaces.