This thesis concerns stressed spline structures. A spline is defined as `an initially straight member with identical second moment of area about any axis perpendicular to its centroidal axis, bent into a spatial curve'. An analytical proof is presented to show that the spline's torsional stiffness is of no importance in its analysis (provided construction details do not introduce any torsional moment). This paramount proof allows the formulation of a spline analysis that relies solely on three translational degrees of freedom (3DOF) per node. Applying this 3DOF analysis to unstrained curves and battened or hoop supported membranes is approximate since the bending stiffness would correspond to one direction only. A series of four test cases validates the proposed 3DOF analysis. The analysis is first applied to a laterally loaded spline ring, where solution convergence and the effect of unequal length segment modelling are investigated. Most significantly, this test case demonstrates that the spline ring has a greater out-of-plane stiffness than a pre-bent ring. This feature lies at the basis of spline stressed membranes - the spline has superior out-of-plane stiffness under the action of forces applied by the membrane. The second and third test cases -- buckling of elastica and of a shallow sinusoidal arch -- clearly demonstrate that the 3DOF analysis is much faster, more accurate, and produces results closer to the analytical values compared with a 6DOF analysis. The fourth test case proves the efficiency of the 3DOF analysis through investigating buckling behaviour and loads of four circular arches under radial loading. As the torsional stiffness does not enter the 3DOF analysis, the stiffness of a spline constructed of spliced segments is identical to that of a continuous spline. In order to demonstrate their feasibility, five medium span (161n-32m) Glass Fibre Reinforced Plastic (GFRP) and one large span (57nt) steel tensegrity stressed spline membranes are designed, form-found and analysed under realistic loading conditions. These design studies show firstly that the spline and membrane stresses occurring under loading are within acceptable material limits and secondly that buckling occurs at values much higher than those encountered in reality. This thesis has demonstrated that engineered stressed spline structures, for which the development of a 3DOF was essential, have great design potential.