Utilising high speed pulsed lasers, crystal growth velocities in excess of 250 m s(-1) can be achieved in metallic systems. At such high growth rates it becomes pertinent to question the assumptions implicit within the Fourier model of thermal conduction. Specifically, the Fourier model allows an infinite velocity of propagation for heat. The rapid solidification problem is posed within a hyperbolic conduction model, imposing a finite velocity of propagation on the heat transfer process. We find that dendritic solidification is only possible if the growth velocity is less than half the thermal wave velocity, C. The likely value of C is discussed.