A new theoretical based model of mass diffusion from an external constant source, through a membrane, into an enclosure and at a constant temperature is developed. Exact solution is presented of one dimensional transient Fickian diffusion equation with initial and boundary conditions appropriate for the mass diffusion into an enclosure. The present model has many practical applications. it may be used as a working tool in diffusion experiments in selecting membrane materials, saving experimental time and cost, predicting the shelf-life of pre-packaged food, drugs and other vulnerable materials to external effects. A good agreement of the model is shown with existing data. The economic advantage of the present model is illustrated by offering shorter experimental time by an order of magnitude. The use of theoretical results minimizes the exposure time to dangerous concentrations of hazardous materials during the experiments. Analysis of the model provides simple linear relationships between various parameters of the mass diffusion into an enclosure.