The epoxidation of vegetable oils is a chemical or biochemical reaction where oil triglycerides are converted into more reactive molecules. These will be further transformed into a broad variety of products with significant potential for industrial applications. The epoxidation of vegetable oils consists of a commercially established process that uses homogeneous mineral acids as catalysts. In this paper, different strong acidic ion exchange resins were evaluated as alternatives to substitute the commercial homogeneous catalysts. Amberlyst 39 was selected as the most promising one to explore the effect of the variables such as temperature, acetic acid, or hydrogen peroxide concentration in sunflower oil epoxidation. The optimal operational conditions that maximized the conversion and oxirane yield were determined. Then, these values were applied in several catalyst reuses for establishing the resin durability. Results show that by employing ion exchange resins, excellent product yields and selectivity are obtained, minimizing post-reaction purification needs.