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``Shear softening" refers to the observed reduction in shear modulus when thestress on an amorphous solid is increased beyond the initial linear region.Careful numerical quasi-static simulations reveal an intimate relation betweenplastic failure and shear softening. The attaintment of the steady-state valueof the shear modulus associated with plastic flow is identified with apercolation of the regions that underwent a plastic event. We present anelementary ``two-state" model that interpolates between failed and virginregions and provides a simple and effective characterization of the shearsoftening.

Percolating Plastic Failure as a Mechanism for Shear Softening in Amorphous Solids