Abstract: Artificial assumptions are needed to set the generalized stress paths in hollow cylinder apparatus (HCA). The resulting limitations to imitate the generalized stress paths in HCA are analyzed. According to the function that GCTS HCA-100 can apply axial loads, torques, inner and outer pressures independently, the method that can determine the external loads directly by the target generalized stress path is put forward. In this way, the generalized stress paths of arbitrary form are presented by the exactly mathematical derivation, and the feasibility is verified by tests. The typical features of the generalized stress path tests are analyzed in 3-D coordinate system b-σ-τ. Based on the cyclic principal stress rotation stress path with constant q, the relationship between the inner and outer pressures and the generalized stress paths is discussed. The controlling process of HCA is simplified and improved, and it may provide a theoretical basis for future tests.