The purpose of this thesis was to:-investigate the properties of the rivers and determine their evolution for large slope-from 0.01 to 0.04 rad;-study the properties of rivers on Titan and to investigate their evolution and to compare them with the rivers on Earth;-explore the terrestrial rivers flowing through the basaltic sediments;-consider the classification of the rivers, including the attempt to apply and modify the current classification.The work involved the use of numerical simulations as the basic research method. The package CCHE2D developed by the scientists from University of Mississippi has been adapted and utilized. It is based on depth averaged two-dimensional Navier-Stokes equations and a three dimensional, convective-diffusion equation of the sediment transport.The first part of the simulations consisted in verifying the applicability of the package to required tasks. The next point was to determine the appropriate flow and transport parameters needed for the simulation that would fit the current knowledge of Titan. The numerical simulations were carried out and their results were visualized and analyzed. The results obtained were also confronted with existing publications and data.Calculations were performed for different simulation times and different river geometries. The initial, up to a few days, simulations were made for the East Fork river geometry. They aimed to discern the dependence of model behavior on considered parameters. Further simulations lasted up to 22-66 days. The purpose of this part was to test whether the assumed geometry of the river allows to transform the river into another type and under what conditions it is possible. The next stage was simulations up to about 240 days, carried out for the river's geometry with a neutral shape that does not impose a subsequent evolution of the river. Other differences were the sediments consisting of grains of the same size and the use of a few different sediment materials. Simulations were made in the case of Earth-for quartz and basalt and for water. In the case of Titan- for water ice and liquid corresponding to the Titan’s rain. It was found that three different liquids for Titan give similar flow qualities. Secondly, the suspension load is the main way of transporting sediments in rivers on Titan. Both the suspension and the bed load are important on Earth, with the bed load being significantly higher than on Titan. The simulations show that different types of rivers could developed for the same conditions on Earth and Titan. This result encouraged to investigate the conditions in which various types of rivers occur, especially the single- and the multiple-channel rivers. Two methods have been used to classify rivers obtained in long simulations: 1) temporal and spatial variations in the river, 2) values of the braiding parameter. Many rivers obtained in long simulations constitute transitional rivers. Comparisons with the publications show that the first method gives the results closer to the field classification, while the second method gives results less expected. The results allowed to draw conclusions about the improvement of river classification rules. It was pointed out the need to take better account of the evolution of the river in the classifications. Moreover, it is shown that determination of the type of the river should be done by considering behavior of the river during some characteristic time scale and/or spatial scale. An attempt was made to determine these scales based on the parameters used in the model.In conclusion, this work deepens the understanding of the processes that shape Titan's surfaces, points to the similarities and differences in the evolution of the rivers on Titan and Earth. Moreover it extend our understanding of rivers for large slope of the channel and for basaltic sediments. It attempts also to address the drawbacks of some river classifications, and suggests ways to improve them.