Response surface methodology was used to model the effect of citric acid, sodium citrate, sodium pyrophosphate, and NaCl on the total volatile basic nitrogen, instrumental texture, pH, and cooking yield of refrigerated and frozen squid. Citric acid reduced total volatile basic nitrogen and pH, increased toughness, and decreased cooking yield. Sodium pyrophosphate and sodium citrate increased the pH and improved the cooking yield. NaCl did not have a significant effect in the presence of the other additives. An optimisation study was conducted in order to minimise total volatile basic nitrogen, maximise cooking yield, and keep texture characteristics at desired levels simultaneously. The optimal solution included 0.044 M citric acid and 0.20 M sodium citrate for the refrigerated product and 0.20 M sodium citrate and 0.012 M pyrophosphate for the frozen product.