Considerable efforts have been devoted to the design of low-power digital electronics. However, after decades of improvements and maturation, CMOS technology could face an efficiency ceiling. This is due to the trade-off between leakage and conduction losses inherent to transistors. Consequently, the lowest dissipation per operation remains nowadays few decades higher than the theoretical Landauer's limit (3 zJ at 300 K). Adiabatic CMOS architectures are good candidates for reducing the dynamic losses. But adiabatic operation reduces operating frequency, thus exacerbating the leakage loss. Consequently, transistors could not be the appropriate support for adiabatic logic. In this paper, we bring in a new paradigm for computation. The elementary device which replaces transistor is based on coupled moving masses suspended by springs. Such objects can be fabricated with MEMS in order to provide a relatively high computing speed (in the order of 1 MHz for a micrometerscaled device). In this paradigm, the logic states are encoded mechanically instead of electrically. The computation is performed by means of electrostatic interactions between the moving elements. We show how they can be arranged in order to create combinational logic gates that can be cascaded. Information is injected and extracted electrically, thus allowing compatibility with conventional circuits. We estimate resistive and damping dissipation of the system via electromechanical simulations, for the case of an AND gate. When the gate is driven adiabatically, the energy per operation drops in the range of the attojoule, even with a micrometer-scaled elementary device. This dissipation almost vanishes for lower frequencies of operation. This suggests that electromechanical adiabatic computing (EMAC) could be able to approach Landauer's limit. EMAC could be valuable for devices operating under high energy constrains with low computing power requirements, such as future massively spread environmental sensors.