Nanomechanical sensors have gained significant attention as powerful tools for detecting, distinguishing, and identifying target analytes, especially odors that are composed of a complex mixture of gaseous molecules. Nanomechanical sensors and their arrays are a promising platform for artificial olfaction in combination with data processing technologies, including machine learning techniques. This paper reviews the background of nanomechanical sensors, especially conventional cantilever-type sensors. Then, we focus on one of the optimized structures for static mode operation, a nanomechanical Membrane-type Surface stress Sensor (MSS), and discuss recent advances in MSS and their applications towards artificial olfaction.