Orthopyroxene is an important mineral in petrologic models for the upper mantle. Its elastic properties are fundamental for understanding the chemical composition and geodynamics of the upper mantle. Here, we calculate the elastic properties of orthoenstatite, the Mg end-member orthopyroxene under upper-mantle pressure and temperature conditions using first principles calculations with LDA. Bulk and shear moduli increase non-linearly with pressure at mantle temperatures, but the shear modulus and VS show very weak pressure dependence in comparison with VP. Compared to other major minerals in the upper mantle, orthoenstatite has the lowest VP, VS, and VP/VS ratio down to the depth of approximately 300 km. The enrichment of opx in the upper mantle can cause the unusually low VP/VS observed in the mantle wedge.