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• Biphasic model, pseudohomogenous with respect to the catalyst, was proposed. • It encompasses the influence of oil fatty acid composition on the process kinetics. • The effect of the process conditions on the epoxidation of linseed oil was studied. • The obtained experimental data were successfully described with the proposed model. • Partition coefficient for acetic acid in a relevant quinary system was determined. The epoxidation of vegetable oils with percarboxylic acids yields commercially applicable green products/precursors for the polymer industry. A reliable model of this reaction system could help to improve the quality of the produced epoxidized vegetable oils. A biphasic model, pseudohomogenous with respect to the catalyst, was proposed for the vegetable oil epoxidation with peracetic acid formed in situ in the presence of an ion exchange resin. The model takes into consideration the influence of the oil fatty acid composition, as an important property of this renewable raw material, on the kinetics of the process. Non-edible linseed oil was chosen for the study since it contains significant amounts of different unsaturated fatty acids, i.e. , linolenic (54.8%), linoleic (16.0%) and oleic (19.8%) acids, in its triglycerides. The effects of temperature (333–358 K), molar ratio of linseed oil double bond:hydrogen peroxide (1:1.1–1:1.5), catalyst amount (10–20 wt%) and reaction time (1–17 h) on the relative epoxy yield and the process selectivity were investigated. The proposed model explained the experimental data concerning changes in double bond and epoxy group amounts during the linseed oil epoxidation with a standard deviation of less than 0.024. The partition coefficient for acetic acid between the liquid phases of the reaction system, as the thermodynamic constant in the model, was separately determined for the linseed oil-epoxidized linseed oil-acetic acid-hydrogen peroxide-water system. Its values ranged from 0.0705–0.3159. The kinetic study showed that one double bond per linolenic acid chain has significantly higher reactivity towards the epoxidation reaction compared to other double bonds in the linseed oil triglyceride. The reactivity difference between these double bonds increased from 6.5 to 41 times with the temperature rise from 333 to 358 K. [ABSTRACT FROM AUTHOR]