The pitting corrosion resistance of AL-6XN PLUS™ superaustenitic stainless steel, 304L, 316L, and 317L austenitic stainless steels was investigated using the cyclic polarization technique. These materials were evaluated in the as received condition and heat-treated at temperatures between 500 °C and 900 °C for 72 h. A thermodynamic simulation was performed using the software Thermocalc® to predict possible deleterious phases in selected temperatures. The simulations have predicted the sigma phase in the selected temperature range. An aqueous solution of sulfuric acid and sodium chloride was used as electrolyte in the corrosion tests. The results showed that pitting corrosion was not observed on the samples of AL-6XN PLUS™ steel. The 304L steel suffered pitting corrosion. All the polarization curves of this steel showed hysteresis characteristics of pitting corrosion. The 316L and 317L steels were resistant to pitting corrosion, but susceptible to crevice corrosion.