We have developed a computer program for estimating the properties of basement rocks surrounding subseafloor boreholes into which (or from which) fluids flow as a result of differential pressure conditions. These flows occur because holes are overpressured or underpressured relative to ambient hydrostatic conditions, and/or because of a pressure imbalance that is created when holes are drilled and cold seawater is injected as a drilling fluid. The new program uses a Markov Chain Monte Carlo (MCMC) approach linked to analytical models of flowing wells to condition estimates of formation properties, including permeability, to borehole thermal data. The analytical models are based on (1) the thermal influence of transient downhole or uphole flow; (2) pressure differences between the borehole and ambient formation associated with observed and inferred thermal conditions; and (3) rates of flow into or out of the borehole at depth as a result of radial flow to or from the formation, based on the transient pressure response. The three analytical models have been used previously to fit hypothetical thermal profiles to borehole observations, but this is generally done with a fixed set of formation and borehole parameters. When run as part of a Markov Chain, the same models are used to find solutions to the inverse problem, but yield distributions of parameters that provide an acceptable fit to observed thermal profiles. We applied the model to two data sets collected soon after drilling that were interpreted in previous studies, from Ocean Drilling Program Holes 504B (southern flank of the Costa Rica Rift, downward flow) and 1026B (eastern flank of the Juan de Fuca Ridge, upward flow), yielding most likely flow rates of approximately 140 m/hr and approximately 200 m/hr, respectively. These flow rates are somewhat higher than rates found in previous studies, suggesting higher permeabilities than previously inferred ( approximately 2X10 (super -11) m2 and approximately 3X10 (super -11) m2, respectively). The new models include estimates of formation permeability distributions, which help to assess the uncertainty in this important property. We have applied the model to new thermal data collected from Holes 1301A and 1301B, and resulting flow rates and permeabilities are consistent with estimates made with packer experiments and from cross-hole pressure response.