Soft structures with rationally designed architectures capable of large, nonlinear deformation present opportunities for unprecedented, highly tunable devices and machines. However, the highly dissipative nature of soft materials intrinsically limits or prevents certain functions, such as the propagation of mechanical signals.Here we present an architected soft system composed of elastomeric bistable beam elements connected by elastomeric linear springs. The dissipative nature of the polymer readily damps linear waves, preventing propagation of any mechanical signal beyond a short distance, as expected. However, the unique architecture of the system enables propagation of stable, nonlinear solitary transition waves with constant, controllable velocity and pulse geometry over arbitrary distances. Because the high damping of the material removes all other linear, small-amplitude excitations, the desired pulse propagates with high fidelity and controllability. This phenomenon can be used to control signals, as demonstrated by the design of soft mechanical diodes and logic gates.soft | mechanical signal | stable propagation | instability S oft, highly deformable materials have enabled the design of new classes of tunable and responsive systems and devices, including bioinspired soft robots (1, 2), self-regulating microfluidics (3), adaptive optics (4), reusable energy-absorbing systems (5, 6), structures with highly programmable responses (7), and morphological computing paradigms (8). However, their highly deformable and dissipative nature also poses unique challenges. Although it has been demonstrated that the nonlinear response of soft structures can be exploited to design machines capable of performing surprisingly sophisticated functions on actuation (1, 2, 9), their high intrinsic dissipation has prevented the design of completely soft machines. Sensing and control functionalities, which require transmission of a signal over a distance, still typically rely on the integration of stiff electronic components within the soft material (10, 11), introducing interfaces that are often a source of mechanical failure.The design of soft control and sensing systems (and, consequently, completely soft machines) requires the ability to propagate a stable signal without distortion through soft media. There are two limiting factors intrinsic to materials that work against this: dispersion (signal distortion due to frequency-dependent phase velocity) and dissipation (loss of energy over time as the wave propagates through the medium). Dispersion can be controlled or eliminated through nonlinear effects produced via the control of structure in the medium (12). For example, periodic systems based on Hertzian contact (13-15), tensegrity structures (16), rigid bars and linkages (17), and bistable elastic elements (18) can behave as nondispersive media, with the nonlinearity of their local mechanical response canceling out the tendency for the signal to disperse at sufficiently large amplitudes. However, dissipation is still an ov...