The main goal of this study is to introduce a stochastic extension of the already existing cutting force models. It is shown through orthogonal cutting force measurements how stochastic processes based on Gaussian white noise can be used to describe the cutting force in material removal processes. Based on these measurements, stochastic processes were fitted on the variation of the cutting force signals for different cutting parameters, such as cutting velocity, chip thickness, and rake angle. It is also shown that the variance of the measured force signal is usually around 4–9% of the average value, which is orders of magnitudes larger than the noise originating from the measurement system. Furthermore, the force signals have Gaussian distribution; therefore, the cutting force model can be extended by means of a multiplicative noise component.