The differences in the evolution of rivers on Earth and on Titan are investigated. Dynamical analysis of the rivers was performed using a numerical package CCHE2D developed by the National Center for Computational Hydroscience and Engineering, University of Mississippi. The model is based on the Navier-Stokes equations for depth-integrated two-dimensional turbulent flow and the three-dimensional convection-diffusion equation of sediment transport. The model enables investigation of the evolution of rivers as a function of total discharge and other parameters of the river. Series of short (from one to several hours) and long (up to 67 days) simulations were performed. We have found that three different liquid hydrocarbons considered for Titan’s rivers give similar velocity fields. It was also found that the suspended load is the main means of transport in Titan’s rivers, while in terrestrial ones, for the same discharge, the bedload could be of the same order as suspended load. Moreover, we suppose that for specific boundary conditions, the evolution of rivers on the Earth promotes the development of braided rivers, while for the same conditions evolution on Titan favours regular meandering rivers.