This article focuses on cutting force modelling in the orthogonal turning of two commonly used types of fibre-reinforced plastic materials. Uncoated cutting tool inserts made of sintered carbide and with different rake angles were used for the designed experiments. In addition to the different rake angles in the experiments, there were also different feeds per revolution and cutting speeds. It was found that the effect of the feed per revolution and the rake angle on the cutting force is statistically significant for both materials. On the other hand, the effect of the cutting speed on the cutting force is statistically insignificant. Therefore, a mathematical model of the cutting force with the impact of the feed per revolution as well as the rake angle was developed and based on the experimental data all constants needed for the proposed mathematical model were found. Based on the comparison of the calculated and experimental cutting forces it was found that there was no statistically significant difference between them, and the proposed model can be therefore considered sufficiently accurate in the given range of the cutting conditions.