The notion of mechanical computation has been revived in the past few years, with the advances of nanofabrication techniques. Although electromechanical devices are inherently slow, they offer zero or very low off-state current, which reduces the overall power consumption compared to the fast complementary-metal-oxide-semiconductor (CMOS) counterparts. This energy efficiency feature is the most crucial requirement for most of the stand-alone battery-operated gadgets, biomedical devices, and the internet of things (IoT) applications, which do not require the fast processing speeds offered by the mainstream CMOS technology. In particular, using Micro-Electro-Mechanical (MEM) resonators in mechanical computing has drawn the attention of the research community and the industry in the last decade as this technology offers low power consumption, reduced circuit complexity compared to conventional CMOS designs, run-time re- programmability and high reliability due to the contactless mode of operation compared to other MEM switches such as micro-relays. In this thesis, we introduce digital circuit design techniques tailored for clamped-clamped beam MEM resonators. The main operation mechanism of these circuit blocks is based on fine-tuning of the resonance frequency of the micro-resonator beam, and the logic function performed by the devices is mainly determined by factors such as input/output terminal arrangement, signal type, resonator operation regime (linear/non-linear), and the operation frequency. These proposed circuits include the major building blocks of any microprocessor such as logic gates, a full adder which is a key block in any arithmetic and logic operation units (ALU), and I/O interface units, including digital to analog (DAC) and analog to digital (ADC) data converters. All proposed designs were first simulated using a finite element software and then the results were experimentally verified. Important aspects such as energy per operation, speed, and circuit complexity are evaluated and compared to CMOS counterparts. In all applications, we show that by proper scaling of the resonator’s dimensions, MHz operation speeds and energy consumption in the range of femto-joules per logic operation are attainable. Finally, we discuss some of the challenges in using MEM resonators in digital circuit design at the device level and circuit level and propose solutions to tackle some of them.