This paper deals with the path planning of non-holonomic vehicles on an uneven natural terrain. It uses the properties of incompressible viscous fluid fields. The full configuration is considered including position and orientation. Lanes are computed instead of a single path. Bounds on curvature and constraints on initial and final orientations are also addressed. By using the Keymeulen/Decuyper fluid method and adding friction forces in the Stokes' equations, the shortest paths or the minimum energy ones can be found, even on an uneven terrain. In addition, in order to satisfy the kinematics and dynamics constraints of a non-holonomic robot a local variation of the shear constraint is used to control the upper bound of the trajectory curvature. Adding small corridors at the departure and destination also satisfies initial and final orientation requirements.