In this paper proposed is a method of estimating the coefficient of earth pressure at rest in the granular or powder material which is supposed to lie in the state of elastic equiliblium. On the basis of an assumption that a relation equivalent to the Hvorslev's equation for the shear strength of saturated clays will come into existence not only in the state of plastic equiliblium but also in the one of elastic consolidation equiliblium, a theoretical equation was obtained by considering the equiliblium of stresses on a special plane, so called the mobilized plane, in the element of material. This proposed equation is characterized by the fact that we can consider the influence of stress history of material. The following conclusions were derived from the several calculation results of the proposed equation. (1) As the effective internal friction angle mobilized at the consolidation equiliblium state approaches at the value of plastic failure state, so the K₀-value becomes smaller. (2) The larger the mobilized cohesive component during the consolidation equiliblium state is, the smaller the K₀-value at the same value of effective friction angle inclines to become. (3) The K₀-value of over-consolidated material in the active state increases a little with increasing over-consolidation ratio.