Based on the non-Fourier heat transfer theory, non-equilibrium theoretical models during rapid solidification process (RSP) of metals are put forward and simulations are done for melt spinning of pure aluminum and laser surface remelting and solidification of pure nickel and aluminum, which include establishing the non-Fourier equations of the processes, non-Fourier simulation of heat transfer and phase transformation during the processes. Simulation results show that RSPs of the metals is within the range of transient heat transfer and the non-Fourier effects can be characterized by the non-Fourier heat transfer modes: (1) When a droplet falls on the surface of a running roller under the condition of melt spinning, the larger the interface heat transfer coefficient, the faster the interface cooling rate and interface velocity. When the interface heat transfer coefficient is the same, with the solid/liquid interface elevation, the interface cooling rate increases and then decreases, which is different from that obtained by Fourier model. In addition, the calculated cooling rate is less than that by the Fourier model; (2) Under the condition of laser heating, the solid/liquid interface velocity increases rapidly and then becomes slow. The simulation results also show the superheating and undercooling of the metals are related to their thermophysical properties.