MUM: flexible precise algorithm for the muon propagation

We present a new muon propagation Monte Carlo FORTRAN code MUM (MUons+Medium) which possesses some advantages over analogous codes presently in use. The most important features of the algorithm are described. Data on the test for algorithm accuracy are presented. Contributions of different sources to the resulting error of simulation are considered. Selected results obtained with MUM are given and compared with ones from other codes.