As regards to daily developments in technology, applications of carbon nano tubes (CNTs) in manufacturing of many devices and equipment are widely promoted. Many sensors, nanomachines, and enhancement of oil, petrochemical and aerospace technologies are some of CNTs applications. With regard to importance and a wide range of these applications, recognition and investigation of CNTs behavior is extremely significant. CNTs have a little curvature naturally, hence they are predominantly subjected to different transverse loads. In this research, based on nonlocal elasticity theory, possibility of snap_through and bifurcation behaviors of arch shaped CNTs due to sinusoidal load distribution and on elastic foundation, are investigated and corresponding graphs are plotted. To obtain buckling critical loads, essential stability equations are derived. Finally the results of classic theory are compared with the results of nonlocal theory and it is indicated that the dimensionless scale parameter(λ), has a key effect on possibility of happening of the buckling and its type. According to the results and plotted graphs, in most cases, increase in dimensionless scale parameter(λ) has leaded to increase the possibility of bifurcation phenomena and some other cases, helped to transition from snap_through to bifurcation, meaning that the possibility of happening of the snap_through phenomena has been declined.