It is well known that tensile residual stresses can be highly detrimental for several functional aspects, such as fatigue life, corrosion and wear resistance, etc., whereas compressive residual stresses are usually considered to have a positive influence on these aspects. The residual stresses that can be found in a mechanical component are mainly generated in the final steps of the machining process. The level of the generated residual stresses depends on the machined material and on the process parameters used. Therefore, the enhancement of the reliability and longevity of a part imposes that a lot of attention is paid to the residual stress problem in the process parameter selection. Unfortunately the mechanism of residual stresses generation is still not completely clear, and a relationship between process parameters and residual stresses is missing. Consequently, the parameter selection is still performed without considering the residual stress problem. The overall goal of the present paper (in two parts) is to identify an analytical relationship between residual stresses and turning process parameters, accounting also for the material being machined. This relationship is the basis for the optimal parameter selection to enhance the longevity and reliability of a part. Following an empirical approach, in the first part of the paper the process parameters that influence residual stresses are identified for three different steels with large differences in mechanical properties. The effect of feed rate, nose radius, entrance angle and depth of cut is investigated using the DOE and ANOVA techniques applied to X-ray diffraction measurements of residual stresses. Results show that the depth of cut does not influence the level of residual stresses, while the main role is played by feed rate and nose radius, and a mild influence is exerted by entrance angle. These results are consistent with the three steels investigated, suggesting that the mechanism of residual stress generation is influenced by process parameters in a common way. An analytical predictive model was then identified for the three steels, including the most relevant process parameters. In the second part of the paper, the influence of the machined material is empirically assessed.