A quantitative magnetic model of Long Valley, California, shows that the magnetic field above this caldera is dominated by intracaldera Bishop tuff, part of the ash flow tuff whose eruption precipitated the caldera collapse. We propose that about half of the 350 km3 of intracaldera Bishop tuff, or that part beneath the resurgent dome, has been subjected to extensive hydrothermal alteration. The heat that produced this alteration is apparently associated with the residual magma chamber, and much of the formation may still be hot (>200¿C). The magnetic minerals in the remaining intracaldera Bishop tuff have not been drastically altered, presumably because the tuff was not heated sufficiently. As a result, the tuff may not be very hot today. The model also reveals the existence of parts of two large precaldera mountains beneath the caldera fill. The resolving power attained in this investigation was possible because we were dealing with large, magnetically distinct lithologic units and a large amount of geological and geophysical data were available constraints to produce the solution.