S U M M A R Y High-resolution magnetic data and potential field methods have been used to perform a detailed analysis of networks of late Quaternary subglacially cut tunnel valleys (central Viking Graben, Norwegian sector of the North Sea). High-frequency, ribbon-like, sinuous, paired magnetic anomalies interpreted to be the signature of tunnel valleys are identified. Such magnetic anomalies have 1-8 nT amplitudes and reflect a magnetic susceptibility contrast between valley infills and the host sediments. Fractional vertical derivative and horizontal gradient transforms provide the best control on the accurately delineation of tunnel valleys by plotting automatically the extrema. The 2-D forward modelling is a very effective approach to determine the geometric parameters and magnetic susceptibility of the modelled valleys. It allows us to determine the finite-width flat horizontal thin geometry as the most appropriate simple geometry to simulate the magnetic anomaly linked to a channel structure. The application of Euler deconvolution using complex algebra allows us to substantiate the structural index (n = 1.5) for simple palaeovalley geometries and to determine fair valley depth estimates.