We discuss a backward Monte-Carlo technique for muon transport problem, with emphasis on its application in muography. Backward Monte-Carlo allows exclusive sampling of a final state by reversing the simulation flow. In practice it can be made analogous to an adjoint Monte-Carlo, though it is more versatile for muon transport. A backward Monte-Carlo was implemented as a dedicated library: PUMAS, providing a detailed muon transport engine down to a few MeV. It is shown for case studies relevant for muography imaging that the implemented forward and backward Monte-Carlo schemes agree to better than 1%. Within these schemes, the achieved accuracy is similar to the one obtained using a detailed Monte Carlo engine (Geant4) but with a significant speedup, at least two orders of magnitude in backward mode.