This paper presents the results of a research study undertaken to assess the variability and model the distribution of R.M.S. surface roughness values obtained in fine turning of AISI 4140 steel using cemented carbide tools of 1/32 in. nose radius. Work specimens of about 30 in. length and 3/2 in. diameter were utilized for the experimental work. Three cutting tools were used making use of one cutting edge in each tool. Each cutting edge was used to fine turn about 15 work specimens. An analysis of variance was performed to ensure that there was not any significant difference in the surface roughness values generated by the three cutting tools. In modelling the distribution of surface roughness values chi-square and Kolmogoroy-Smirnov goodness of fit tests were applied.