The inverse problem is defined here as follows: determine the transmissivity at varius points, given the shape and boundary of the aquifer and recharge intensity and given a set of measured log‐transmissivityYand headHvalues at a few points. The log‐transmissivity distribution is regarded as a realization of a random function of normal and stationary unconditional probability density function (pdf). The solution of the inverse problem is the conditional normal pdf ofY, conditioned on measuredHandY, which is expressed in terms of the unconditional joint pdf ofYandH. The problem is reduced to determining the unconditional head‐log‐transmissivity covariance and head variogram for a selectedYcovariance which depends on a few unknown parameters. This is achieved by solving a first‐order approximation of the flow equations. The method is illustrated for an exponentialYcovariance, and the effect of head and transmissivity measurements upon the reduction of uncertainty ofYis investigated systematically. It is shown that measurement ofHhas a lesser impact than those ofY, but a judicious combination may lead to significant reduction of the predicted variance ofY. Possible applications to real aquifers are