SHAFT79 (Simultaneous Heat And Fluid Transport) is an integrated finite difference program for computing two-phase non-isothermal flow in porous media. The principal application for which SHAFT79 is designed is in geothermal reservoir simulation. SHAFT79 solves the same equations as an earlier version, called SHAFT78, but uses much more efficient mathematical and numerical methods. The present SHAFT79 user's manual gives a brief account of equations and numerical methods and then describes in detail how to set up input decks for running the program. The application of SHAFT79 is illustrated by means of a few sample problems. (MHR)