Lyophilization (also known as freeze drying) is a process that is commonly used to increase the stability of drug products, e.g., mRNA vaccines, in pharmaceutical manufacturing. While extensive efforts have been dedicated to shift the pharmaceutical industry towards continuous manufacturing, the majority of industrial-scale lyophilization is still being operated in a batch mode. This article proposes the first mechanistic model for a complete continuous lyophilization process, which includes freezing, primary drying, and secondary drying. The state-of-the-art lyophilization technology is considered, in which vials are suspended and moved continuously through the process. The model can describe the evolution of several critical process parameters, namely the product temperature, ice/water fraction, sublimation front position, and concentration of bound water, for the entire lyophilization process. The model is also demonstrated for several applications related to process design and optimization. Ultimately, the framework and results presented in this work can serve as a solid foundation to guide the design and development of future continuous lyophilization processes.