In Cu-Ni-Al shape memory alloy, we observed a significant size effect on the twinning stress, i.e. the dependency of compression stress needed for twin-variant reorientation on sample size using in situ loading of micro- and nanoscale pillars in scanning and transmission electron microscopes. With decreasing dimensions of pillars, the twinning stress sharply increases following scaling power law with an exponent approximately n=-2/3. For very small nanopillars, the projected twinning stress is so high that the nanopillars are deformed by plastic deformation instead of twinning. Our results shed light on some of the fundamental aspects of nanoscale behaviour of shape memory alloys which is important for applications in microelectromechanical systems.