Natural convection within inclined high aspect-ratio rectangular cavity was analysed by using finite element method. For a cavity of sapect-ratio 20, the flow patterns of secondary vortices and the heat transfer characteristics on the wall were obtained with the variation of tilt angle as well as Ra and Pr. The observation on the governing equations shows that the increase of Ra/Pr and the existence of nonzero tilt angle make the flow pattern more complicated and so it becomes difficult to obtain converging solution. The max. value of Ra/Pr attained in this study was 3x10$^$4/at 0$^$0/ tilt angle and 1.1x10$^$4/ at 45.deg. tilt angle for aspect ratio 20and Pr=0.7. Finally an empirical formula for Nusselt number which can accout for the effect of tilt angle is obtained for laminar flow regime.