The author discusses the numerical solutions of nonlinear hyperbolic partial differential equations with source terms arising from environmental problems. These source terms describe the interaction with the surrounding medium which dominates the fluid flow and characterizes the well-balanced states. The author presents numerical methods, which are able to reproduce these states or at least to give stable solutions. Firstly, the scalar one-dimensional problem \(u_t+u(u+a)_x=0\) with prescribed initial data \(u_0\) and a special form of \(a\) is considered. The numerical scheme analysed uses a splitting technique and leads to unstability or to very small mesh sizes. Thus, the author proposes other methods for solving the problem. Namely, a Riemann solver including the source term enables the use of finite volume schemes (e.g. Godunov scheme) with a CFL condition independent of the source term. The method works in the multidimensional case, too.