Electromagnetic multisheet modelling is a powerful tool for large model areas, if they can be approximated by a multilayered heterogeneous conductivity structure of small vertical dimension in comparison with the penetration depth of electromagnetic fields. In this paper, thin sheet technique is applied to the whole Fennoscandian (Baltic) Shield, whose upper mantle conductivity structure is the objective of the long period electromagnetic array experiment BEAR (Baltic Electromagnetic Array Research). Three thin sheets, each of about 120,000 model cells with the base length of 10 km, describe a-priori crustal inhomogeneities in terms of conductances. The three sheets represent i) upper crust from surface to the depth of 10 km including continental and ocean bottom sediments and seawater, ii) middle crust ranging from 10 km to 30 km and iii) lower crust from 30 km to 60 km. Thus, modelling is taking into account distortions caused by crustal conductivity anomalies. Additionally, distortions due to inhomogeneous external current systems are investigated by introducing an equivalent current system of a polar electrojet model at ionosphere height. Modelling results are illustrated by induced current distribution at different depth levels and by various electromagnetic transfer functions. The latter demonstrate the resolution of crustal conductivity anomalies and their screening effect even at long periods. The predicted behavior of transfer functions in the very complex conductivity structure is compared with the experimental BEAR data, showing qualitatively a first order agreement for most of the sites. Modeled phases for periods of a few thousands of seconds are considerably biased in comparison with experimental data if the background 1-D model has monotonously decreasing resistivity. However, the bias from phases is removed if a conducting asthenosphere having a resistivity of 20 Ωm is emplaced between the depths of 200 km and 300 km. Thus, multisheet modelling indicates a well conducting upper mantle under the Fennoscandian Shield. All modelling has been performed using a multisheet code by Avdeev, Kuvshinov and Pankratov.