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As it is getting increasingly difficult to achieve gains in the density and power efficiency of microelectronic computing devices because of lithographic techniques reaching fundamental physical limits, new approaches are required to maximize the benefits of distributed sensors, micro-robots or smart materials. Biologically-inspired devices, such as artificial neural networks, can process information with a high level of parallelism to efficiently solve difficult problems, even when implemented using conventional microelectronic technologies. We describe a mechanical device, which operates in a manner similar to artificial neural networks, to solve efficiently two difficult benchmark problems (computing the parity of a bit stream, and classifying spoken words). The device consists in a network of masses coupled by linear springs and attached to a substrate by non-linear springs, thus forming a network of anharmonic oscillators. As the masses can directly couple to forces applied on the device, this approach combines sensing and computing functions in a single power-efficient device with compact dimensions.