We investigate the dynamics of conduction band electrons interacting with strong laser pulses. Time evolution of the reciprocal space electron distribution is described using an appropriate version of the Boltzmann equation. Although state of the art laser sources can be powerful enough to drive wave packets through the boundaries of the first Brillouin zone—i.e. they can induce dynamical Bloch oscillations—relaxation mechanisms can inhibit the appearance of this fundamental effect. The main source of relaxation in our model is the scattering interaction with longitudinal optical phonons. We find that signatures of dynamical Bloch oscillations are still visible even in the presence of realistically strong scattering.