A new type of finite element model, called the double mesh model is proposed in this thesis. With the level of free expansion as the input, the model is able to simulate the restrained ASR expansion by taking into account the effects of physical restraints. The retrained ASR expansion in reinforced concrete cubes and beams are simulated. Numerical expansion obtained from this new model showed a good agreement with the experiments. Then, the expanded beams are loaded in shear to simulate the shear behaviour of ASR affected concrete beams. In this new model, ASR damage is embedded through a realistic simulation of ASR expansion. Whereas, in the traditional method, ASR damage is taken into account by a direct reduction of the input material properties and the expansions are not simulated. According to the data obtained from experiments, even though the mechanical properties of concrete are reduced due to ASR, but this not necessarily leading to the decrease in the capacity of the beams. In some experiments the change of failure mode is observed where the unaffected beam failed in shear but the ASR affected one failed in bending. This is because in ASR affected beams, the increase in shear load results in the enlargement of the existing ASR cracks instead of generating new diagonal shear cracks, and thus the shear failure is prevented. In the precracking method, the effects of ASR cracks on the capacity and the failure mode are taken into account in the model since the ASR cracks are simulated. Whereas, in the traditional method, where the ASR damage is included through the reduction of the input properties, the effects of ASR cracks are not able to be reflected in the model.