Observations have revealed that standing and propagating kink oscillations are ubiquitous in the solar corona, providing the opportunity to use these oscillations as a seismological tool. We perform numerical simulations of transverse waves propagating in a low beta plasma. When density structuring is present, kink and Alfvén modes become coupled in inhomogeneous regions. The frequency-dependent decay of propagating kink waves is observed as energy is transferred to the local Alfvén mode. We also consider mechanisms for generating standing transverse oscillations.