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. SHAFT 79 solves the same equations as an earlier version, called SHAFT78, but uses much more efficient mathematical and numerical methods. The physical model employed in both SHAFT78 and SHAFT79 is discussed in Pruess et al., 1979 a, b. Some pre- and post- processor programs used with SHAFT78 and SHAFT79 are described in the SHAFT78 user's manual (Pruess et al., 1979a). 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; further examples of application are provided in Pruess et al., 1979c, and Pruess and Schroeder, 1979