This paper proposes the application of kriging to estimate the mean areal precipitation (MAP) of mountainous regions under two different assumptions of the drift and spatial dependency of precipitation influenced by orographic effects. The “detrending” method assumes a linear relationship between the drift and the ground elevation. The variogram is computed from the residuals resulting after subtraction of this linear relationship from the original data. The generalized covariance (GC) procedure, on the other hand, assumes a polynomial drift with unknown coefficients and a generalized covariance estimated directly from the raw data. The automatic structure identification procedures under GC assumptions performed by the program BLUEPACK on the data from nine storms in the San Juan Mountains, northwestern Colorado, identified only one case of a nonstationary drift. Kriging with the GC's identified produced MAP estimates which were consistently lower than the “detrending” estimates and agreeing closely to Thiessen polygon estimates. Point kriging tests indicate that the “detrending” procedure performs better than the GC method in terms of providing accurate kriged estimates but are less successful in representing the kriging estimation error variance. The test results from the one case of a nonstationary drift identified by the GC procedures also show inconsistency between actual errors and the kriging estimation variance. Both methods, “detrending” and the procedure assuming generalized covariances of order k, are feasible practical methods of estimating the MAP of mountainous areas, the “detrending” procedure performing better in terms of providing accurate MAP estimates. The results presented show again that the kriging estimation error variance is dependent on the structural model adopted for the drift and variogram. In general, caution is warranted in using the kriging variance because of this fact. In particular, the “detrending” kriging estimation variance has been shown to be of doubtful consistency in several cases and similary for the one GC of order 1 studied in this work.