Stellar shells observed in many giant elliptical and lenticular as well as a few spiral and dwarf galaxies, presumably result from galaxy mergers. Line-of-sight velocity distributions of the shells could, in principle, if measured with a sufficiently high S/N, constitute one of methods to constrain the gravitational potential of the host galaxy. Merrifield & Kuijken (1998) predicted a double-peaked line profile for stationary shells resulting from a nearly radial minor merger. In this paper, we aim at extending their analysis to a more realistic case of expanding shells, inherent to the merging process, whereas we assume the same type of merger and the same orbital geometry. We use analytical approach as well as test particle simulations to predict the line-of-sight velocity profile across the shell structure. Simulated line profiles are convolved with spectral PSFs to estimate the peak detectability. The resulting line-of-sight velocity distributions are more complex than previously predicted due to non-zero phase velocity of the shells. In principle, each of the Merrifield & Kuijken (1998) peaks splits into two, giving a quadruple-peaked line profile, which allows more precise determination of the potential of the host galaxy and, moreover, contains additional information. We find simple analytical expressions that connect the positions of the four peaks of the line profile and the mass distribution of the galaxy, namely the circular velocity at the given shell radius and the propagation velocity of the shell. The analytical expressions were applied to a test-particle simulation of a radial minor merger and the potential of the simulated host galaxy was successfully recovered. The shell kinematics can thus become an independent tool to determine the content and distribution of the dark matter in shell galaxies, up to ~100 kpc from the center of the host galaxy.
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