A stirred vessel is a device for mixing fluids. It is widely-used in industry and plays an important role in the chemical process. In the stirred vessels, liquid is stirred by the rotational motion of impeller, and often, there exists large deformation of free surface. The moving particle semiimplicit (MPS) method is a meshfree particle method suitable for such complex physical phenomena because moving boundaries can be handled with relative ease. The devolatilization process is one of the applications of stirred vessel, where dissolved volatile components are removed by inducing the nucleation of bubbles in the tank. This paper explains numerical algorithms for the stirred vessel analysis with the MPS method. Furthermore, numerical simulations of the devolatilization process using the MPS method with incorporated bubble models are presented.