In many countries of moderate to high seismicity, reinforced concrete (RC) core walls are used as lateral bracing systems in mid- to high-rise buildings where they typically accommodate lift shafts or stair cases. Unlike planar walls which provide horizontal strength and stiffness mainly in the in-plane direction of the wall, core walls provide bidirectional strength and stiffness. This feature complicates their inelastic behaviour which is not yet fully understood as experimental and numerical studies are still rather scarce when compared to planar walls. Therefore, current design codes are based on findings from planar walls while specific guidelines for the design and analysis of core walls are still lacking. In addition, simple analysis tools widely used by design engineers such as the plastic hinge model, have been derived and calibrated for columns, beams or planar walls and their suitability for core walls has been only marginally verified. For these reasons the current study focuses on: (1) improving the knowledge on the inelastic behaviour of U-shaped walls under bidirectional loading and (2) on extending easily applicable engineering type models, such as the plastic hinge model, to the analysis of U-shaped walls. The scope of the thesis is limited to U-shaped walls, which is the simplest type of core wall that still retains the key characteristics of such walls. The first part of the thesis focuses on understanding the behaviour of U-shaped walls under loading along the geometric diagonal of the section. This loading direction is not typically considered in the design process but it was found to determine the shear design of the flanges while the displacement capacity for this direction might be the lowest of all the loading directions. In order to address the behaviour under diagonal loading, two large-scale quasi-static cyclic tests on U-shaped walls were carried out. Failure mechanisms specific to diagonal loading and possible critical design aspects related to these failure modes were identified from the experimental results. In addition, the influence of the longitudinal reinforcement distribution on the wall behaviour was investigated. The second part of the thesis focuses on adapting equations used in plastic hinge model for the analysis of U-shaped walls. Plane section analyses and a shell element model validated against the experimental data were used to perform parametric studies on U-shaped walls. From the results of the parametric studies a new equation for the yield curvature for any direction of horizontal loading was proposed as well as a modified yield displacement equation that accounts for the partially cracked wall height at yield. With this equation, predictions of yield displacements were improved especially for very slender walls. Quantities that rely on the yield displacement, such as the effective stiffness of the wall were also better predicted when the cracked height was accounted for in the prediction. And finally, plastic hinge length equations were also modified to account for the variation with the different loading directions.