We create acoustomechanical soft metamaterials whose response to uniaxial tensile stressing can be easily tailored by programming acoustic wave inputs, resulting in force versus stretch curves that exhibit distinct monotonic, s-shape, plateau and non-monotonic snapping behaviors. We theoretically demonstrate this unique metamaterial by considering a thin soft material sheet impinged by two counter-propagating ultrasonic wave inputs across its thickness and stretched by an in-plane uniaxial tensile force. We establish a theoretical acoustomechanical model to describe the programmable mechanics of such soft metamaterial, and introduce the first- and second-order tangential stiffness of its force versus stretch curve to boundary different behaviors that appear during deformation. The proposed phase diagrams for the underlying nonlinear mechanics show promising prospects for designing tunable and switchable photonic/phononic crystals and microfluidic devices that harness snap-through instability.