This article presents selected flow modeling indices of the Bystra River catchment area (east Poland) obtained using the SWAT model simulations for three regional climate models driven by the EC-EARTH global climate model for 2021–2050 and both RCP4.5 and RCP 8.5 scenarios. The research area was selected due to the large relief of the terrain, the predominance of soils made of loess and the agricultural nature of the Bystra River catchment area, which is very sensitive to climate change, has very valuable soils, and can be used as a test area for modeling land use-based adaptation measures to climate change. The calibration and validation using the SUFI-2 algorithm in the SWAT CUP program was carried out in order to determine the water balance. After obtaining satisfactory results, the SWAT-CUP program simulated the best parameter values for climate change projections. In analyzed climate projections, the monthly mean sums of actual evapotranspiration and potential evapotranspiration will be higher compared to the simulation period of the 2010–2017 model. The exception is the month of June, where actual evapotranspiration in most climate projections is lower compared to the years 2010–2017. The average monthly total runoff for the Bystra River basin will be lower in most of the 2021–2030 climate change projections for most months compared to the reference period. Also, in the 2031–2040 and 2041–2050 periods, the average monthly total runoff will be lower for the RCP 4.5 scenarios (except for one RCP 4.5 scenario in 2031–2040). Additionally, in the case of the RCP 8.5 for the two scenarios in 2041–2050, the average monthly total runoff will be higher compared to the reference years. We determine that the analysis impact of climate change will result in 31 recognized and different small sub-catchments of the Bystra River, which result from higher precipitation and less evapotranspiration for RCP 8.5 in 2041–2050. All of the above changes in the individual components of the water balance may have a negative impact on the vegetation in the coming decades. The temperature increase and the variable amount of precipitation in individual months may lead to an increased number of extreme phenomena. Increased mean monthly sum of actual and potential evapotranspiration, as well as changes in monthly sums of total runoff, may disturb the vegetation in the studied area at every stage of growth. The above components may also influence changes in the amount of water in the soil (especially during the growing season). Counteracting the effects of future climate change requires various adaptation measures.