This thesis focuses on the numerical modeling of water movement and water storage in municipal solid waste (MSW) landfills. Hydraulic investigations at landfill sites indicate that the water flow is highly non-uniform. Preferential flow paths dominate the water transport. The non-uniform flow regime is caused by the heterogeneous character of the waste material itself, the disposal and compaction procedure, and by the construction elements such as gas wells or daily cover layers. In this thesis a two-dimensional two-domain approach for modeling water flow in landfills has been developed. Thereby a flow field consisting of one vertical favored flow path (channel domain) surrounded by the waste mass (matrix domain) is defined using the software HYDRUS-2D. The water flow model is calibrated using data from two landfill sites in Austria (Breitenau) and Sweden (Spillepeng). Predicted leachate generation corresponds well with the observed discharge. Parameters calibrated and thus heterogeneity of the flow regime is different for the two landfills. In order to quantify the heterogeneity of the flow regime, the transport of highly soluble salts is investigated. The calibrated water flow model and HYDRUS-2D were used to simulate the solute discharge. This allows determining the fraction of waste mass engaged in water flow. For the investigated landfills this fraction varies between 25 % and 50 %. The new model improves prediction of future emissions of MSW landfills, because it allows assessing flows and stocks of water, the key variables in landfills, in a quantitative way.