The structural identifiability properties of the Baranyi model were analyzed in fitting the effect of oregano and thyme essential oils on growth of Salmonella typhimurium in rainbow trout stored under aerobic (AP), modified atmosphere (MAP) and vacuum packed (VP) conditions. Although, formally proven to be structurally identifiable using the Taylor-series approach, the Baranyi model was not practically identifiable in the presence of experimental data. In addition, performance of the Baranyi model was compared with those of the empirical modified Gompertz and logistic models and Huang models. Higher values of R(2), modeling efficiency and lower absolute values of mean bias error, root mean square error, mean percentage error and chi-square were obtained with modified Gompertz and logistic models than those obtained with the Huang and Baranyi models. The essential oil and packing treatments had remarkable delaying effects on the growth of S. typhimurium. Considering the obtained results in this study, the empirical modified Gompertz and logistic models can be used more effectively than the mechanistic Huang and Baranyi models to predict the effect of plant essential oils on growth potential of Salmonella in fish products stored under aerobic, MAP/VP conditions.