Two formulations for determining the minimal risk path of a vehicle through a minefield are considered and compared. Firstly, by following a calculus of variations argument a system of four coupled ODEs are derived. These are solved via a shooting method and computational difficulties encountered in this process are discussed. Secondly, the trajectory of the vehicle is approximated by a discrete (but large) system of coupled springs and masses resulting in a large but well behaved system of ODEs to solve. Numerical solutions to this system are investigated. The strengths and weaknesses of each approach are discussed.