Using an Almost Ideal Demand System food price elasticities for German households are calculated. These elasticities serve as a basis to simulate the effect of the substitutions of different food types due to a tax on saturated fat. The change of food structure causes effects on the energy and nutrient supply of individuals as well as, on consumer welfare. These effects are analyzed for different German household groups. It is found that decreases in energy and fat intake are small but potentially effective especially for low-income households. However, due to the collateral decrease of nutrients which Germans have deficient supply of, the total health effects of a fat tax remain unclear. Furthermore the results show that low-income groups would bear higher welfare losses than high-income groups. Due to these results and the fact that a fat tax is not an efficient measure to reduce the negative welfare effects of overweight, other measures to reduce overweight should be taken into account.