One of the proposed damping mechanisms of coronal transverse loop oscillations in the kink mode is resonant absorption as a result of the spatial variation of the Alfvén velocity in the equilibrium configuration. Analytical expressions for the period and the damping time exist for 1-D cylindrical equilibrium models with thin non-uniform transitional layers. Comparison with observations indicates that the assumption of thin non-uniform transitional layers is not a very accurate approximation of reality. This contributions starts with a short review of observations on transverse oscillations in solar coronal loops. Then it presents results on periods and damping times of resonantly damped kink mode oscillations for (i) fully non-uniform 1-D cylindrical equilibrium models in which the equilibrium quantities vary in the radial direction across the magnetic field from the centre of the loop up to its boundary and (ii) non-uniform 2-D cylindrical equilibrium models in which the equilibrium quantities vary both in the radial direction across the magnetic field and in the axial direction along the magnetic field. An important point is that the periods and damping times obtained for these fully non-uniform models can differ substantially from those obtained for thin non-uniform transitional layers. This contribution then reports on a consistency test between theory and observations showing that there is a very good agreement within the observational inaccuracies.