Abstract Rare-earth Barium Copper Oxide (REBCO) high-temperature superconducting (HTS) magnets are typically fabricated by winding REBCO tapes into coils. During operation, these magnets experience compressive stresses induced by winding tension, electromagnetic forces, and thermal contraction, which can cause mechanical deformation and fracture. Conventional approaches estimate the mechanical properties of REBCO tapes based on the behavior of individual constituent materials; however, such estimates are valid only for single tapes. In practical applications, stacked or wound tapes exhibit markedly different mechanical responses due to interfacial effects. Therefore, investigating the mechanical behavior of stacked HTS tapes is essential for reliable structural design and analysis. In this study, five types of REBCO tapes were selected and cut into uniform dimensions to fabricate stacked specimens. Compression experiments were conducted in a liquid-nitrogen-filled vacuum chamber at two maximum stress levels to simulate typical stresses experienced during magnet cool-down and operation. Two stacking configurations were considered: one consisting solely of REBCO tapes and the other composed of alternating REBCO and stainless-steel tapes, commonly referred to as metal insulation. Precision cutting tools were employed to minimize edge effects, and custom specimen guides and load transfer blocks were designed to ensure proper transversal loading. A cryogenically compatible universal testing machine was used to apply compressive stress, while an extensometer measured the displacement. Each specimen underwent three loading–unloading cycles to evaluate hysteresis behavior after local post-yield. Stress–strain curves were obtained, and the effective tangent modulus was determined. Under maximum compressive stress, the measured modulus varied significantly depending on the specimen, ranging from 1.3 GPa to 62.9 GPa, and exhibited clear stress-dependent behavior. The copper stabilizer thickness ratio, associated with low stiffness, strongly influenced both the strain and tangent modulus. These results provide key mechanical properties necessary for the structural evaluation and modeling of HTS magnets.