This doctoral thesis discusses various approaches to modeling flow in rivers with floodplains. Measurements on a physical hydraulic model of the Sava River with distinctive floodplains provided noteworthy data which were used for a detailed numerical analysis of the flow interaction between the main channel and floodplains. Turbulence models incorporated into the mathematical model PCFLOW2D, which was developed more than two decades ago and is continuously being improved at the Chair of Fluid Mechanics with Laboratory, Faculty of Civil and Geodetic Engineering, University of Ljubljana, were precisely analyzed and modified. By analyzing the impact of a single term in a momentum two-dimensional time-averaged Navier-Stokes (Reynolds) equation, which describes the depth-averaged flow, it has been shown that in cases of flows in large water bodies, use of an appropriate turbulence model does not play an essential role because the influence of turbulence can be sufficiently covered through the friction term. Therefore the flow in a vertical slot fishway, where turbulence is very pronounced and its accurate modeling is of great importance was investigated. For this particular case, the sensitivity analysis was carried out for the recently integrated Smagorinsky turbulence model. Analysis has shown that, in order to achieve good agreement of numerical results with measurements, it is necessary to calibrate the Smagorinsky coefficient Cs. This is a new discovery, as to our knowledge all previous studies and other numerical programs recommended an equal value (or within a very small interval) of the coefficient Cs for all types of flow. Our analysis showed that the value of the coefficient Cs is highly dependent on the applied numerical grid and individual type of flow and can significantly deviate from the previous reference values. With the detailed sensitivity analysis of parameters of the mathematical model, progress has been made in understanding the issues addressed, which should in the future allow easier and faster calibration of mathematical models and greater confidence in the obtained results.