The steady two-dimensional flow of a horizontal heat pipe in vapor region is investigated numerically. For study of heat transfer and fluid flow behaviors of the heat pipe, the governing equations in vapor region have been solved using a finite difference method. The numerical results of heat transfer and fluid flow are presented for Reynolds numbers ranging of (Re =4, 10), the Prandtl number taken is (Pr=0.00368), and the pipe dimension is taken to be (L/R =5). The results show that the stream function at the wall increases linearly in the evaporator, decreases linearly in the condenser and is steady in the adiabatic region because of uniform inflow and outflow boundary conditions. Also, it can be seen that as the Reynolds number increases, the pressure distributions shift up without considerable change in their shapes. The numerical analysis have shown that for the low and moderate Reynolds number, the shear stress becomes zero at a point very close to the end of the condenser. For verification of current model, the results of stream function for a heat pipe have been compared with the previous study at the same boundary conditions and a good agreement has been noticed.