  We present a 3D Bayesian method to model the kinematics of strongly lensed
galaxies from spatially-resolved emission-line observations. This technique
enables us to simultaneously recover the lens-mass distribution and the source
kinematics directly from the 3D data cube. We have tested this new method with
simulated OSIRIS observations for nine star-forming lensed galaxies with
different kinematic properties. The simulated rotation curves span a range of
shapes which are prototypes of different morphological galaxy types, from dwarf
to massive spiral galaxies. We have found that the median relative accuracy on
the inferred lens and kinematic parameters are at the level of 1 and 2 per
cent, respectively. We have also tested the robustness of the technique against
different inclination angles, signal-to-noise ratios, the presence of warps or
non-circular motions and we have found that the accuracy stays within a few per
cent in most cases. This technique represents a significant step forward with
respect to the methods used until now, as the lens parameters and the
kinematics of the source are derived from the same 3D data. This enables us to
study the possible degeneracies between the two and estimate the uncertainties
on all model parameters consistently.
