This paper is devoted to investigation of laser cleaning of paper with fat-containing contaminations. In recent years, laser technologies have been widely used in the preservation of Cultural Heritage (CH). One of the main fields of  laser application in this area is the cleaning of CH objects from natural and anthropogenic contaminations. It is known that there exist two main approaches to the laser cleaning, e.g. dry cleaning and wet cleaning. We will present experimental results of wet laser cleaning with the Ytterbium fibre laser (wavelength of 1064 nm) of fat-containing contaminations from model samples and fragments of a real historical artefact such as XIXth century book.