In the framework of continuum mechanics, Hill's Condition of Stability can detect unstableequilibrium of a strain-stress state. The use of a distinct element method is proposed to study the relation betweena discrete form of Hill's Condition of Stability and the instability in granular medium. The reference 2Ddiscrete material is composed of piled up wooden cylinders. Two different expressions of discrete second orderwork, based on a particle or contact description, are used. The numerical results show that the spatial andtemporal variations of the second order works for both particles and contacts are very close. Moreover thebursts of kinetic energy are correlated spatially and temporally with negative values of the second order work(for both expressions).