The huge transverse Lorentz force experienced by CORC cable during the operation of fusion projects may cause irreversible degradation of its current-carrying capacity. Therefore, it is particularly important to study the influence of cable parameters on their transverse compression performance, and use these influence laws to adjust cable parameters to improve the critical value of transverse compression load that CORC cables can withstand. Solid copper bar former CORC cables with a former diameter of 5.57 mm are produced using HTS (high temperature superconducting) tapes (manufactured by Shanghai Superconductor) of 4 mm and 5 mm width respectively. The experimental results show that the CORC cable wound with 5 mm wide HTS tape has a greater critical transverse compression load than the cable wound with 4 mm wide HTS tape. This indicates that using wider HTS tapes to wind CORC cables can effectively improve their transverse compression performance. A solid copper bar former CORC cable and a stainless steel spiral tube former CORC cable are also produced. Through transverse compression experiments, it is found that the critical transverse compression load of the solid copper bar former and the stainless steel spiral tube former CORC cable are 130 kN/m and 89 kN/m, respectively. This indicates that the solid copper bar former CORC cable has better transverse compression performance. In addition, we also compared the influences of flat and arc pressure blocks on the transverse compression performance of CORC cables, and this experimental results provided a basis for the selection of the bobbin structure when using CORC cables to make coils.