The author studies probabilistic inventory models of multi-period with discrete demand, in which a method is shown to get an optimal policy and the influence of demand distribution on the optimal policy has also been investigated. On the other hand we have developed the theory of probabilistic inventory models with a piecewise cost function under continuous demand. A lot of properties of an optimal policy in its inventory system are obtained. As this application a method is presented in this paper to get an approximation of an economic order quantity in multi-period inventory problems provided the demand subjects to a continuous distribution. For that sake we assume some conditions on the total cost function of single period. The amount of an economic order quantity depends heavily on the properties of a demand distribution and we shall show it numerically in the inventory examples.