The Cutting slope is to be minimized when a tunnel meets the contour of slope terrain at a right angle around its portal. However, a tunnel portal has been generally installed at a right angle to the longitudinal axis of a tunnel with no consideration of the intersection angle with the slope terrain. This sometimes tended to cause huge cutting slope that resulted in many disadvantage in terms of safty, economy and environment. Therefore, the minimization of cutting slope is studied by taking the intersection angle into account, and the result is compared with that by the conventional method. In addition a design method for the inclined portal to the tunnel axis is proposed through 3D-FEM analysis, also the applicable ground condition is suggested.