Effectiveness of a generalized plate finned-tube heat exchanger is calculated by numerical methods by changing shapes of fin and arrangements of tubes. An alternative refrigerant R134a is taken in this study. In calculating effectiveness in a generalized plate finned-tube heat exchanger, conduction between neighboring tubes is taken into account in addition to convection between fin and surrounding fluid. Governing equations are obtained by using energy balance in a differential control volume in a tube. An elliptic equation solver for three dimensional problems, EL3D, is used. In this study, conduction effect is investigated in single-phase and two-phase flows with various fin shapes and arrangements of tubes. Reduction of effectiveness by perforation is studied too. According to the results of this study, perforating fin, increasing the number of tubes, and increasing the distance between neighboring tubes enhance effectiveness of a generalized plate-finned tube heat exchanger.