As fossil fuel reserves are rapidly being depleted, sustainable alternatives have to be found to fulfil the world's energy demand. Numerous concepts have been proposed to generate electricity by harnessing renewable energy sources such as solar or wind power. One of these concepts is the the so-called solar updraft tower (SUT). The SUT consists of three elements: a solar air collector, wind turbines and a chimney. The taller the chimney, the larger the stack effect and thus the more energy which can be generated by the turbines. The proposed concepts for this chimney schematise it as a reinforced concrete cylindrical shell, with the bottom half shaped like a hyperboloid and the top half as a flared cylinder, outfitted with ten stiffening rings evenly distributed over the height. Chimneys as tall as 1500m have been proposed, and, previous research shows that these tall structures have very low eigenfrequencies which come very close to the peak of the wind power spectrum. This makes them extremely vulnerable to resonance induced by storm actions. Two types of resonance can be distinguished in these structures; along-wind resonance, and across-wind resonance. Along-wind resonance is caused by turbulence in along-wind gusts. The second type, across-wind resonance, is caused by the alternating shedding of vortices. This leads to pulsating excitation forces in the across-wind direction, and, if the frequency of the vortex shedding is the same as one of the eigenfrequencies of the chimney, resonance will occur. In this thesis, a finite element model is created based on a pre-existing design. This so-called base model is then analysed to determine which key problem areas could benefit from improvement. The analyses show that especially the first two eigenfrequencies are critical for along-wind resonance as well as across-wind resonance. These eigenfrequencies are seen as two individual problem areas as improvements to one eigenfrequency not necessarily guarantee improvements to the second eigenfrequency. Furthermore, tension on the windward side leads to cracks in the stiffening rings which negatively influence the eigenfrequencies and thus the dynamic response. The last area which could benefit from optimisation is the cost of the chimney; an optimal solution does not use more material than necessary. A design tool called SUMAT (Solar Updraft Modal Analysis Tool) is created which enables the user to analyse multiple chimney configurations at once, subsequently being able to compare their results. Various sensitivity analyses are carried out to determine the influence of geometric and material parameters on the four key problem areas of the chimney. A multi-objective optimisation process is followed to optimise each of the key problem areas, ie. objective functions, by hand. The first step in optimising the structure is to subdivide the parameters which were researched into four categories, depending on their usefulness. The second step consists of gradually introducing these parameter changes into the base model. The optimisation process revealed that the objective functions can be maximised as follows: increasing the moment of inertia of the rings by changing their aspect ratio ensures that the chimney is fully loaded in compression. An increase in the throat height further improves the reduction of tension on the windward side and the first eigenfrequency. A reduction in wall thickness at the top of the chimney improves the first eigenfrequency while also reducing material use. Lastly, it appears that the stiffening rings at the bottom serve little to no purpose. Removing them leads to a reduction in material use while some of the material gained can be used to increase the dimensions of the top rings, consequently improving the second eigenfrequency and reducing tension. More thorough analyses revealed that the optimisation process has indeed led to an overall improved structure when compared to the original base model. While along-wind resonance does not pose as great a threat as was initially assumed, due to the influence of aerodynamic admittance, the results do show that the improved eigenfrequencies led to a smaller increase in deflection as a result of dynamic wind action. Vortex shedding also no longer poses a threat as the improved second eigenfrequency resulted in critical wind speeds which are much larger than could ever occur at the chosen reference location. Future optimisations should therefore focus more heavily on the second eigenfrequency than on the first, assuming that the accompanying mode shapes stay the same.