The uncertainty in the boundary of two-dimensional, steady state well catchments due to the uncertainty of the spatially variable hydraulic conductivity field is investigated. The well discharge rate and the areal recharge rate are assumed constant. The catchment boundary is traced by backward particle tracking in the velocity field. The uncertainty bandwidth of the catchment boundary is approximated in first order by formulating the time-dependent longitudinal and transversal second moments of the particle displacements along and normal to the mean particle trajectory. Applications of the approach are presented for a set of simple configurations. The results are compared with the results from unconditional numerical Monte Carlo simulations. The comparison allows an assessment of the accuracy, the applicability, and the limits of the method. The approximation corresponds quite well with the Monte Carlo simulations provided that the distance to the domain boundary is sufficiently large.