The study of the properties of the materials used in the several fields of the mechanical industry requires an analysis of their mechanical characteristics and behaviour under load, or under a combination of loads, which produce multiaxial stress states on the machine components. The analysis of the behaviour under axial and torsional combined loads, either static or time-variable, proves particularly interesting. During combined loads tests, the test machine should not transmit any parasitic action to the specimen, such as shear and bending moment, in order to consider only the reaction to torsion and axial load. Furthermore, it should allow to apply the torsional and axial actions separately (the application of axial loads must not be influenced by the applied torque and vice-versa). The test machine must also be designed to apply a high torsional moment without producing any non-allowable deformation. This paper reports the results of a survey of universal multiaxial test machines frames for performing torsion, static or fatigue tests on cylindrical specimens, with the simultaneous application of axial, tensile or compression loads, either static or time-variable. A preliminary survey showed that traditional test machines are equipped with a plane frame that cannot withstand a high torsion. A new machine was therefore developed based on a study to provide the most suitable frame structure to withstand a high torsion. The machine was patented.