Rarefied gas flow and heat transfer in the rectangular, trapezoidal, elliptical and circular micro-channels are investigated numerically in the slip-flow regime. A control-volume based numerical method is used to solve the Navier–Stokes and energy equations with velocity-slip and temperature-jump conditions at the walls. Effect of various parameters such as Reynolds number (from 0.1 to 1), channel aspect ratio (from 0.2 to 1), and Knudsen number (less than 0.1) on the velocity, pressure and temperature fields were examined., Also variation of parameters such as hydrodynamic and thermal entrance length, friction factor, Nusselt number, efficiency and thermal resistance of micro-channels with different cross sections are studied too. Comparison of the results with no slip and no jump condition showed that in the entrance region of all cross sections, a very large reduction in the friction factor and Nusselt number are obtained. This reduction is due to the rarefaction effects. There is a finite asymptotic value for the friction factor and Nusselt number at the channel inlet. This asymptotic limit is observed for any geometry at any value of Reynolds number. As it is evaluated at a location where fluid is about to enter the channel, and therefore, there is no recognition of the geometry and Reynolds number yet. In this region when the no-slip boundary condition is applied, strong pressure gradients that exist near the walls causes the maximum velocities to be found near the walls rather than in the channel core as would normally be expected. But the slip condition reduces the amount of pressure generated as a result of the slowing down of the fluid particles at the wall and therefore the maximum velocities near the walls decrease. As flow approaches the fully developed region the maximum velocities are found in the channel core which is due to reduction of the pressure gradients in the cross section. Applying temperature-jump at the wall reduces the heat transfer rates, and therefore, lowers the fluid temperature as compared to the no-slip/no-jump conditions. The best efficiency in these cross sections is for a elliptical cross section at the Re=0.3 , Kn=0.1 and ? =1/3 whit the maximum heat transfer rates and minimum pressure reduction. Key words Slip-flow, Temperature-jump, Rarefaction, Rectangular micro-channel, Trapezoidal micro-channel, Elliptical micro-channel, Circular micro-channel, Entrance region, Friction coefficient, Heat transfer coefficient.