The off-centre displacement delta of a Li ion in KTaO₃ and the surrounding lattice distortion is calculated using a nonlinear shell model developed for the pure lattice. The method of the static lattice Green function is applied and the range of the Li dipole forces is limited to a few lattice constants. A short range Li-O interaction potential is used which leads to a lithium displacement in reasonable agreement with estimations made from NMR measurements. A lattice polarisation is found to develop in a region around the Li, whose total dipole moment exceeds by a factor of 4.5 that arising from the Li displacement itself. This is in satisfactory agreement with the observed dielectric properties. The shape of the polarised region is strongly anisotropic, the longer axis being coincident with the (incipient ferroelectric) polar axis.