Crystals of potassium aluminium sulfate with different thicknesses were grown using the standard growth technique in view of investigating the optical power limiting properties of the crystals. The transmission of the optical power pumped with a laser was measured for various thicknesses of the crystals. It was found that there is an optical power limiting activity for potassium aluminium sulfate crystals. An overall quadratic dependence of output power on input power was obtained for thick samples. However, for thin samples, the dynamic limit and saturation were very clear. The dynamic range was found to be smaller for crystals with higher thicknesses. It was also found that the sharpness of the dynamic range increases with decreasing the crystal thickness. The results were discussed on the basis of the reverse-saturable absorption, which is usually considered as a dominating limiting mechanism in heavy-molecular systems.