Measuring the compressive behaviour of sheet materials is an important process for understanding the material behaviour and numerical simulation of metal forming. The application of side force on both surfaces of a specimen in the thickness direction is an effective way to prevent buckling when conducting compressive tests. However, the side effects of side forces (such as the biaxial stress state and non-uniform deformation) make it difficult to interpret the measured data and derive the intrinsic compressive behaviour. It is even more difficult for materials with tension–compression asymmetry such as steels that undergo transformation-induced plasticity. In this study, a novel design for a sheet compression tester was developed with freely movable anti-buckling bars on both sides of the specimen to prevent buckling during in-plane compressive loading. Tensile and compressive tests under side force were conducted for low-carbon steel using the digital image correlation method. The raw tensile and compressive stress–strain data of the low-carbon steel showed apparent flow stress asymmetry of tension and compression, originating from the biaxial and thickness effects. A finite element method-based data correction procedure was suggested and validated for the low-carbon steel. The third generation advanced high strength steels showed intrinsic tension–compression asymmetry at room temperature whereas the asymmetry was significantly reduced at 175 °C.