In river and tidal stream power assessment, uncertainties arise from model assumptions and the inexact specification of physical and numerical model parameters. Combined, such uncertainties can greatly affect power estimates for a given site. The thesis examines the effects of bed roughness and turbine drag uncertainties on turbine power estimates. An analytic model is developed for transfer of bed friction uncertainty to power extracted from turbines in a strait, representative of a river. A validated finite volume solver of the shallow water equations is developed and applied to simulate flow driven by a constant head difference through a one-dimensional strait. The presence of a turbine fence is included using enhanced bed friction. A parameter study examines the effect of uncertainty propagation from bed friction to power. Excellent agreement is obtained between the analytic and numerical power uncertainty estimates for a given input bed friction PDF. Perturbation methods are used to determine the leading-order effect of bottom friction uncertainty in tidal stream power assessment. The theoretical models consider quasi-steady flow in a channel completely spanned by tidal turbines, a similar channel but retaining the inertial term, and a circular turbine farm in laterally unconfined flow. It is found that changes to expected power depend on the dynamic balance in the channel, the turbine configuration, and the geometry of the site considered. Bottom friction uncertainty increases estimates of expected power in a fully-spanned channel, but has the reverse effect in laterally unconfined farms. The optimal number of turbines under bottom friction uncertainty is lower for a fully-spanned channel and higher in laterally unconfined farms. The effect of uncertainty in turbine drag is also considered. A standard methodology is presented for uncertainty propagation using general computational models. The methodology is tested using a shallow flow model of the Pentland Firth, where power statistics are determined according to input bed friction probability distribution, and the results compared against those from the (simplified) analytic perturbation approaches. Although the analytic models for channels perform reasonably well regarding the estimate of expected power, the predictions from the unconfined analytic model were not so satisfactory owing to the model assumptions. The methods for uncertainty transfer presented in the thesis could readily be applied to many other problems encountered in hydraulic engineering, such as river flow routing, urban flood risk, reservoir sedimentation, etc.