This paper deals with the dispersive behaviour of the waves in a traction-free plate, commonly referred to as the Rayleigh–Lamb (R–L) waves, considering the effect of strain gradient elasticity (SGE) and the velocity gradient kinetic energies. The SGE is modelled using the generalized first strain gradient theory (GFSGT) involving three independent material length constants. The transcendental equations in terms of the frequency and wavenumber, for the symmetric and anti-symmetric modes of the shear horizontal (SH) and plane (P & SV) R–L waves are derived here, separately. The dispersion curves for the frequency and the velocity are obtained by solving these equations numerically. This study is also extended for a plate subjected to mixed-boundary conditions. The observations presented here illustrate the significance of gradient elasticity over the behaviour of the elastic wave propagation in micro and nano-plates. © 2019