Various cabling methods for HTS flat tapes have been developed in the past few years. We have been developing a REBCO tape cabling method twisting a stack of tapes (TSTC). TSTC conductors were recently tested at high magnetic fields 4 T-20 T. The test results have shown some significant degradations during high current and high field tests. This paper investigates the mechanical characteristics of a TSTC conductor. Effects of transverse loads on single tapes and TSTC conductors were studied to evaluate and compare their mechanical behaviors. A device was designed to measure the critical currents of tapes and cables at 77 K as a function of transverse load. YBCO tapes from two different suppliers were examined. The mechanical transverse load was applied to TSTC conductors to simulate a load similar to the one caused by the natural electromagnetic load during operations. Taking into account the unique geometrical structure of a TSTC conductor, the effects of localized and uniform transverse loading conditions on a TSTC conductor were investigated. Several TSTC samples including single tapes and cables were tested. The experimental results are presented and discussed in the context of use of this type of conductor for high field magnets applications.