Strongly stratified easterly flow across the Svalbard archipelago is investigated by means of a numerical model with a grid distance of 10 km. Idealized simulations of flow over idealized and real orography with Brunt–Väisälä frequency fixed at N=0.019 s−1 and with a uniform background velocity varying between 8.7 and 26 ms−1 are performed. With a maximum height of the orography at 916 m, the non-dimensional mountain height =Nh/U varies between 0.67 and 2.0. The Rossby number Ro=U/fL is of order unity. Robust features of these simulations are an upstream velocity minimum south of Hinlopenstretet and a downstream wake to the north of Isfjorden. Over the downslopes, upstream of the wake, the velocities are high in the simulations at the lower end of due to vigorous gravity wave activity. As is increased towards 2.0, the gravity wave activity in this area is greatly reduced, and the associated velocity maximum disappears. Downstream jets are radiating from the three resolved fjords Isfjorden, van Mijenfjorden and Hornsund, and the two former jets merge into one further downstream. The absolute velocity maximas are found in the south, where the velocities are enhanced relative to the upstream undisturbed velocity by factors of 1.7 to 2.2. The highest velocities are recognized to be associated with the gravity wave activity. However, velocities are generally high in the south due to the left–right asymmetry induced by planetary rotation. The simulation of a real case largely confirms these findings. In this case wind speeds reaching between 35 and 40 ms−1 are simulated near the southern tip of Spitsbergen. An investigation of the zonal wind speeds at Spitsbergen is also presented and reveals that from 1990 to 1997, 13 situations with upstream wind speed of the same strength as in the case study have occurred.