Reducing the scale of the power engines, pose problems that are not encountered at large scale. Several effects, which are negligible at large scale, prove to dominate these viscous forces driven flows. Particularly, it is useful to investigate unsteady machines at small scales when subject to pressure waves. In this paper, the effects of scale on the propagation of shock waves in narrow shock tubes are studied using analytical and numerical modeling approaches. It is discussed how the size scale can become a decisive factor in governing the behavior of these small-scale devices. The results, in agreement with previous studies, suggest that the wall viscous stresses and heat conduction lead to deviation in flow characteristics compared to ideal shock wave behaviors observed in larger scales. The numerical results show shock-wave attenuation along the length of a narrow shock tube, in accordance with the developed analytical models. The obtained results can be useful in determining how much performance of micro wave machines can be influenced by the effects of scale.