Oscillatory pumping tests consist of injecting periodic discharge into an aquifer and measuring head response along vertical piezometers surrounding the well. The aim is to identify the specific storativity s and conductivity K of the aquifer, which are generally spatially variable. Recently, an analytical solution for oscillating head in a homogeneous formation was derived and applied to the Boise aquifer test site (Rabinovich et al., 2015). Equivalent properties seq, Keq , were identified by best fit of the computed and measured heads. Here, this approach is generalized for heterogeneous aquifers of spatially variable logconductivity, which is modeled as a stationary space random function characterized by KG (geometric mean), \(\sigma_Y^2\) (variance), I and Iv (horizontal and vertical integral scales). Semi-analytical solutions are obtained for the mean head amplitude and phase by a first order approximation in variance. Application to a given realization requires a large ratio between the well length and Iv, as well as availability of a large number of measurements (ergodicity). We define a correction term, ψ, representing the impact of heterogeneity on H. Investigating the dependence of ψ upon the distance from the pumping well reveals the existence of a few regimes, namely a near well region in which it is independent of period and far away, where the solution pertains to a homogeneous aquifer of effective properties. The solution is applied to the Boise aquifer test by a best fit of H with the measured head in 3 piezometers, for a given value of \(\sigma_Y^2\) = 0.5. In spite of the departure from ergodicity, the identification of KG is quite robust and in agreement with previous tests while that of I is subject to uncertainty. An additional method for improving the identification of K by conditioning on measured point-wise head (co-kriging) is also outlined.