Aims. Using a model of vertically polarised fast magnetoacoustic waves in curved coronal loops, the method of coronal seismology is applied to observations of transverse loop oscillations. Methods. A coronal loop is modeled as a curved magnetic slab in the zero plasma-beta limit. For an arbitrary piece-wise continuous power law equilibrium density profile, the dispersion relation governing linear vertically polarised fast magnetoacoustic kink waves is derived. The ways in which this model can be used for coronal seismology are explored and applied to two observational examples. Results. The Alfven speed and equilibrium density profile are determined from observations. It is shown that the mechanism of lateral leakage of fast magnetoacoustic kink oscillations described in this model is efficient. In fact, the damping is so efficient that in order to match predicted values with observational ones, either the loop needs to be highly contrasted or the transverse Alfven speed profile needs to be close to linear. Possible improvements to make the modeling of lateral wave leakage in loops more realistic, allowing a lower damping efficiency, are discussed.