This thesis is concerned with the elasto-plastic behaviour of circular rods under combined torsion-tension loading Three aspects of the work were examined. In the first, an instrumented mechanical torque-tension machine was designed, built and commissioned to enable the application of biaxial loading under controlled conditions. The main features of the machine are (1) it can apply either simultaneous or individual loadings subject to a specific deformation history and (11) it provides the time variations of the controlling and the controlled deformation parameters using the appropriate load cells and tranducing elements. Whilst the machine was controlled by analogue signals, it was designed such that it could allow digital control of the different command signals. An analytical model to calculate the stiffness of the machine has been developed. The second was wholly devoted to the experimental investigations where solid, copper and steel, circular rods were subjected to complex non-proportional biaxial loading paths. In these paths, elasto-plastic torsion followed by tension, keeping the angle of twist constant, and elasto-plastic tension followed by torsion, holding the corresponding axial displacement constant, were examined. Other loading paths, where the initial axial loads and the torques were maintained constant, and where the torque and the axial load were applied successively, were also studied. The expenmental programme also considered the biaxial loading of thinwalled steel tubes. In the third, the experimental results were compared with two different analytical models from the literature Numerical solutions were also obtained along the lines descnbed in an available literature. Expenmentally, it has been observed that when the rod is initially subjected to a torque and then, keeping the angle of twist constant, to a gradually increasing axial load, the rod behaves as if its torque carrying ability becomes drastically reduced without in any way affecting its load carrying ability. Similarly, when the rod is initially subjected to an axial load and then, keeping the axial displacement constant, to a gradually increasing torque, the rod behaves as if its load carrying ability becomes drastically reduced without in any way affecting its torque carrying ability Such reductions in the load or torque capacity appear to be governed by the material plastic yield criterion. During the successively applied loading, it has been observed that when the rod is initially subjected to an initial torque and then to a successively applied axial load and torque, keeping the axial displacement or the angle of twist constant in an alternate manner, the rod soon regains its axial load carrying capability irrespective of the initially applied torque. Similarly, during the multiple alterations of successively applied torque or axial load, it has been observed that at any stage for the axial load or torque, whichever was applied subsequently, the rod regains its carrying capability of the parameter involved. Experimental test results with fitted strain gauges show that, even when the angle of twist or axial displacement was held constant, the strain readings increase rapidly with the decrease of the initially applied torque or axial load at the confined zone where the plastic deformation begins. Elsewhere of the specimen the strain readings decrease. The findings of this work have direct bearing on the relaxation of tightening torques or axial loads as experienced by critical engineering components, such as couplings, bolted joints and rotating shafts, which are subjected to similar type of biaxial loadings.