The possibility of using long range ultrasonic guided wave non‐destructive testing for the inspection of metallic structures coated with attenuative layers is extremely attractive. However, the material damping may cause severe attenuation of the acoustic signal, resulting in reduction of the test range. This paper addresses the dispersion of shear horizontal waves propagating in metallic plates coated with viscoelastic layers and the implications for long range testing. © 2004 American Institute of Physics