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Tube hydroforming is a forming method which has several advantages. By using pressure in combination with material feeding it is possible to manufacture products with high structural integration and tight dimensional tolerances. The forming method is especially suited for aluminium alloys which have a relatively low ductility. Finite Element simulations are used extensively in the sheet metal stamping industry, where the methodology has contributed to a better understanding of the process and the new prediction capability has significantly reduced costly die tryouts. Similarly, the tube hydroforming industry can benefit from Finite Element simulations, and this simulation methodology is the topic of this dissertation. Deep drawing and tube hydroforming have a basic difference, namely that the latter process essentially is a force controlled process. This fact, in combination with the anisotropic behaviour of aluminium tubes, enforces a need for accurate constitutive descriptions. Furthermore, the material testing needs to account for the specifics of tube hydroforming. The importance of proper material modelling is in this work shown for hydrobulging and hydroforming in a die with extensive feeding. The process parameters in hydroforming are the inner pressure and the material feeding, where a correct combination of these parameters is crucial for the success of the process. It is here shown, that Finite Element simulations together with an optimisation routine are powerful tools for estimating the process parameters in an automated procedure. Finally, the reliability and quality of the simulation results depend on how failure is evaluated, which in the case of hydroforming mainly oncerns wrinkling and strain localisation. Since tube hydroforming often is preceded by bending operations this fact also demands the criteria to be strain path independent. In this work, it is shown that the prediction of strain localisation depends on the ability to predict diffuse necking, which in turn is strongly related to the chosen constitutive model.