This study investigates the influence of machining parameters for helical interpolation on the accuracy of the shape of holes and their surface quality. The objective is to ensure high-precision hole formation during finish machining. To achieve this, the authors conducted experiments to determine the relationship between roundness and cylindricity deviations and various machining parameters, including helix pitch, feed rate, machining time, and cutter diameter. The research results showed that during the helical milling process the degree of roundness and cylindricity deviations has little dependence on the machining parameters mentioned above. In addition, the authors discovered that on condition of choosing the helix pitch within the range of 0.5–1.1 mm, the increase in milling productivity is negligible, however, the increase in the pitch causes the microrelief parameters of the surface to increase by 1.5–2 times. Summarizing the conducted research, the authors conclude that in order to achieve high accuracy of the shape of holes while maintaining high machining process productivity, the optimal parameters are the maximum feed rate of the equipment with the helix pitch within the range of 0.3–0.7 mm. Moreover, the authors developed an artificial neural network that allows to predict the degree of roundness and cylindricity deviations depending on the machining parameters with 91% validity.