The Ukrainian Government started the process of EU water Directives implementation aimed at developing of the River Basin Management Plan for 9 main river catchments. The program SWAT was tested to simulate the water flow of a large plain river with a predominant snow supply. River discharges (12 gauges), snow cover depth (13 stations), and the soft data, including graphically defined surface runoff and MODIS evapotranspiration, were used to calibrate the model. The calibration flowchart, along with a detailed source data description, is proposed to aid with streamflow simulation for the snowmelt-driven watersheds and fill the existing gap of distributed hydrological modeling in the region. The main issues with snow simulation and climate data coverage are discussed. The program SUFI-2 in SWAT-CUP package was used for performing calibration/validation and uncertainty analysis. The statistics (R2, NSE, PBIAS) showed good agreement (NS > 0.7, R2 > 0.75, PBIAS < ±10%) for a major part of the gauges and satisfactory for all of them (NS > 0.5, R2 > 0.6, PBIAS < ±15%), except of two linked upstream outlets. This study provides the basis for further research on water resources, the impacts of climate change, and water quality issues.