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In this study, the modelling of arithmetical mean roughness after turning of C45 steel was performed. Four parameters of cutting tool geometry were varied, i.e.: corner radius r, approach angle κ, rake angle γ and inclination angle λ. After turning, the arithmetical mean roughness Ra was measured. The obtained val-ues of Ra ranged from 0.13 μm to 4.39 μm. The results of the experiments showed that surface roughness improves with increasing corner radius, in-creasing approach angle, increasing rake angle, and decreasing inclination an-gle. Based on the experimental results, models were developed to predict the distribution of the arithmetical mean roughness using the response surface method (RSM), Gaussian process regression with two kernel functions, the se-quential exponential function (GPR-SE) and Mattern (GPR-Mat), and decision tree regression (DTR). The maximum percentage errors of the developed mod-els were 3.898 %, 1.192 %, 1.364 %, and 0.960 % for DTR, GPR-SE, GPR-Mat, and RSM, respectively. In the worst case, the maximum absolute errors were 0.106 μm, 0.017 μm, 0.019 μm, and 0.011 μm for DTR, GPR-SE, GPR-Mat, and RSM, respectively. The results and the obtained errors show that the developed models can be successfully used for surface roughness prediction. © 2022 Production Engineering Institute. All rights reserved.