An important problem in terrain analysis is modeling how water flowsacross a terrain and creates floods by filling up depressions. This thesis examines a number of flood-risk related problems. One such problem is answering terrain-flood queries: given a terrain represented as a triangulated xy-monotone surface, a rain distribution and a volume of rain, determine which portions of the terrain are flooded. The first part of this thesis develops efficient algorithms for terrain-flood queries under the single-flow direction (SFD) and multiflow-directions (MFD) models, in which water at a point flows along a single downslope edge or multiple downslope edges respectively. Algorithms are given for the more specific case of the SFD model, and then it is shown how to answer queries in the more general case under the MFD model. Available terrain data is also often subject to uncertaintywhich must be incorporated into the terrain analysis. For instance, the digital elevation models of terrains have to be refined to incorporate underground pipes, tunnels, and waterways under bridges, but there is often uncertainty in their existence. By representing the uncertainty in the terrain data explicitly, methods for flood risk analysis that properly incorporate terrain uncertainty when reporting what areas are at risk of flooding can be developed. The second part of the thesis shows how the algorithms for flood-risk can be extended to handle ``uncertain'' terrains, using standard a Monte Carlo method. Finally, the third part of the thesis develops efficient algorithms for computing flow -query related problems to determine how much water is flowing over a given vertex or edges as a function of time. We show how to compute the 1D flow rate as well as develop a model for computing 2D channels as well. A number of the algorithms are implemented and their efficacy and efficiency are tested on real terrains of different types (urban, suburban and mountainous.)