A low computational cost semi-analytical procedure is presented for the solution of incompressible fully developed turbulent flow through symmetric and asymmetric ducts with rough walls. Using a modified algebraic turbulence model to represent the influence of rough surfaces, the flow field in ducts with different wall roughnesses is solved. The velocity distribution and the friction factor in two different geometries, circular duct and parallel plates, are presented and compared with experimental and numerical data available in the literature, and a satisfactory agreement is obtained.