In the present work the problem of optimizing the geometry of tubes with internal asymmetrical fins in order to enhance the hear transfer under laminar flow conditions is studied. The velocity and temperature distributions on the finned tube cross-section are determined with the help of a finite element model and a global heal transfer coefficient; an equivalent Nusselt number and a compared effectiveness are calculated. Polynomial profiles are assigned to the two lateral fin surfaces and the geometry is optimized in order to make the hear transferred per unit of tube length or surface as high as possible for a given weight and for a given hydraulic resistance. The optimum asymmetrical fins, obtained by means of a genetic algorithm, are finally shown for different situations and their performances are compared with those of optimum symmetrical fins,