We describe a three-dimensional numerical inverse model for the interpretation of cross-hole pneumatic tests in unsaturated fractured tuffs at the Apache Leap Research Site (ALRS) near Superior, Arizona. The model combines a finite volume flow simulator, FEHM, an automatic mesh generator, X3D, a parallelized version of an automatic parameter estimator, PEST, and a geostatistical package, GSTAT. The tests are simulated by considering single-phase airflow through a porous continuum, which represents primarily interconnected fractures at the site. The simulator solves the airflow equations in their original nonlinear form and accounts directly for the ability of all packed-off borehole intervals to store and conduct air through the system. Computations are performed in parallel on a supercomputer using 32 processors. We analyze pneumatic cross-hole test data, previously conducted by our group at ALRS, in two ways: (1) by considering pressure records from individual borehole monitoring intervals one at a time, while treating the rock as being spatially uniform, and (2) by considering pressure records from multiple tests and borehole monitoring intervals simultaneously, while treating the rock as being randomly heterogeneous. The first approach yields a series of equivalent air permeabilities and air-filled porosities for the rock volume being tested, having length scales of the order of meters to tens of meters. The second approach yields a high-resolution geostatistical estimate of how air permeability and air-filled porosity, defined on grid blocks having a length scale of 1 m, vary spatially throughout the tested rock volume. It amounts to three-dimensional pneumatic tomography or stochastic imaging of the rock, a concept originally proposed by one of us in 1987. The first paper of this two-part series describes the field data, the model, and the effect of boreholes on pressure propagation through the rock. The second paper implements our approach on selected cross-hole test data from ALRS. ¿ 2001 American Geophysical Union