A packed bed thermal storage has several desirable characteristics to be used for energy storage. The behavior of packed bed is predicted by set of differential equations. A numerical solution is developed for packed bed storage tank accounting to the secondary phenomena of thermal losses and conduction effect. The effect of heat loss to surrounding (K1), conduction effect (K2) and air capacitance (K3) are examined in the numerical solution. It is found that the values of K1 and K2 are small and can practically be neglected in the solution. The solution shows the profiles of air and rock bed temperatures with respect to time and length of bed.