Modern food industries employ either mechanical or cryogenic methods for freezing products. A wealth of literature is available on design, implementation and optimization of mechanical freezing systems in the food industry. Cryogenic freezing is a relatively new technology for the food industry and there is a need for developing mathematical models to characterize this technology. Our focus here is to develop analytical and numerical models for describing the dynamics of the cryogenic freezing tunnel system. Two models for sizing and rating of the tunnel freezer have been developed. A composite model combining the freezer and the food freezing dynamics using a two step finite difference methods has been proposed for sizing the tunnel freezer. The error in prediction the temperature profile of the food material and the tunnel freezer is reduced to less than 5%, consequently reducing cryogen consumption by up to 30%. The proposed model can be useful for minimizing the operating costs of tunnel freezers by deriving suitable control strategies and provide insights for improvements in their design. A dynamic tank model has been developed for rating the tunnel freezer. The tank model guarantees stability of the system, is accurate, and can be readily extended to complex designs and applications where there are multiple zones with nozzles and fans. (c) 2006 Elsevier Ltd. All rights reserved.