In mechanical excavation, the response of the tool forces on the cutterhead is important when the excavation begins in actual cutting conditions because the reliability and efficiency of the cutting machine are influenced directly by the pick performance. The magnitude of the cutting force is utilized to estimate the specific energy, which is calculated from experimental tests to predict the performance of a mechanical excavation machine. However, the magnitude of normal force is also the other key parameter that used to calculate the load of the work unit of excavation machine. Therefore, based on linear rock cutting experiments performed on the low and high strength sandstones, the variation of the normal force and the variation of ratio of normal force to cutting force have been investigated under different cutting angles. The influence of related cutting angles, which have some direct or indirect effects on the normal force, has been discussed in detail. In this context, the attack angles lower than 80°, preferably between 50 and 60°, the clearance angle lower than 10°, resulted in a decrease on the normal forces. Besides, the positive values of rake angles led to more efficient cutting. Furthermore, it was suggested to employ the conical picks having the tip angles lower than 80° in order to obtain optimum cutting conditions. The certain ranges of the relevant angles exhibited the same characteristic both on low and high strength sandstones. As a result, the empirical models, which were found to be statistically significant, were put forward. These results would be essential for the design of the pick and cutterhead.