This paper discusses a generalized method to produce standard foot-trajectories for a quadruped walking vehicle having arbitrary reachable ranges and walking on uneven and inclined surfaces in random posture. The standard supporting foot-trajectories are one of the most basic parameters for the gait control, because the legs have to follow the trajectories as long as the terrain and posture conditions are maintained. The introduced method goes through the processes: 1) projection of the gait scheme on horizontal plane, 2) definition of the effective searching areas, 3) selection of crab-walking pattern between x & y types, 4) generation of the stroke contour maps, 5) selection of the longest stroke and their existing areas. The validity of the proposed method is verified by several computer simulations.