This paper constructs, presents and compares four approximate Riemann solvers for use with solving one-dimensional unsteady free surface flows. These solvers are usually the building blocks towards the construction of higher order accurate shock-capturing schemes. Details of the governing equations are presented. One dimensional dam-break flood wave propagations are analysed to demonstrate the applicability and the validity of the Riemann solvers. A treatment of source terms such as friction, slope and non-prismaticity of the channel is also presented. Computed results obtained with these solvers are compared with exact or published numerical solutions to define their characteristics and give an insight into the limitations of the methods, their relative strengths and weaknesses.