Inventory systems containing products with a fixed shelf life differ fundamentally from conventional inventory systems because physical age affects both availability and economic value. A replenishment policy that is optimal for nonperishable products may generate excessive waste when items expire before demand occurs. This paper develops a mathematical framework for inventory systems with deterministic shelf life, stochastic demand, replenishment lead time, and age-dependent holding and disposal costs. The model represents inventory as an age-structured state variable and derives the associated balance equations, demand fulfillment constraints, expiration dynamics, cost function, and long-run optimization objective. A discrete-age formulation is also developed for computational implementation. The paper further discusses first-expired-first-out issuing, lost sales, backlogging, stochastic demand, and numerical solution methods. A numerical illustration demonstrates the trade-off between product availability and expiration waste. The framework is applicable to food, pharmaceuticals, blood products, chemicals, and other products for which inventory becomes unusable after a prescribed lifetime.