The dispersive behaviour of waves propagating in gradient-dependent an
d rate-dependent media is investigated analytically and numerically. A
ttention is focused on the proper modelling of dynamic strain localisa
tion and the crucial role that dispersion plays in this. By considerin
g the dispersive properties of a continuum and of a modelling in finit
e elements the effect of the discretisation on the localisation phenom
enon can be quantified.