This paper numerically investigates unsteady behavior of cloud cavitation, in particular, to elucidate the induced shock wave emission. To do this, we consider a submerged water-jet injection into still water through a nozzle and make some numerical analysis of two-dimensional multiphase flows by Navier-Stokes equations. In our previous study , we have shown that twin vortices symmetrically appear in the injected water, which plays an essential role in performing the unsteady behavior of a cloud of bubbles. In this paper, we further illustrate the elementary process of the emission of the shock waves. First, we set up the mixture model of liquid and gas in Lagrangian description by the SPH method, together with the details on the treatment of boundary conditions. Second, we show the velocity fields of the multiphase flow to illustrate the inception, growth as well as the collapse of the cloud. In particular, we explain the mechanism of the collapse of the cloud in view of the motion of the twin vortices. Further, we investigate the pressure fields of the multiphase flow in order to demonstrate how the shock wave is emitted associated with the collapse of the cloud. Finally, we show that a small shock wave may be released prior to the main shock wave emission.