It is shown that it is possible to accelerate micro-foils to velocities from 108 cm/s up to relativistic velocities without the disturbance of the Rayleigh-Taylor instability. The acceleration occurs due to the radiation pressure of proper high power lasers. In these systems, the ablation force is negligible relative to the ponderomotive force that dominates the acceleration. The laser irradiances of 1017 W/cm2 < IL < 1021 W/cm2 with a pulse duration of the order of 10 picoseconds can accelerate a micro-foil by the laser radiation pressure to velocities as high as 109 cm/s before breaking by Rayleigh Taylor (RT) instability. Similarly, laser irradiances of IL > 1021 W/cm2 with pulse duration of the order of 10 femtoseconds can accelerate a micro-foil to relativistic velocities without RT breaking. Due to the nature of the accelerating ponderomotive force, in both the relativistic and non-relativistic cases, the structure of the accelerated target contains a double layer (DL) at the interface of the laser-target interaction. The DL acts as a piston during the acceleration process. The influence of the DL surface tension on the RT instability is also analyzed in this paper.