Recently, ultrasound contrast imaging has been improved greatly, because its application of an approach for therapy is urgently required for area of the heart and abdominal. Sonoporation is also one of the applications using microbubbles that attracts attention in the world. There have been so many studies for understanding the mechanism of sonoporation and improving efficiency of ultrasound contrast agents. Nonspherical oscillation is at a stage before the breakup process of microbubbles. Therefore, consideration of a microbubble's nonspherical oscillation is absolutely imperative for its future development. Thus in this thesis, the author regarded microbubbles as two dimensional air-liquid two-phase flow and calculated their dynamics by using Computational Fluid Dynamics (CFD). Numerical calculation of a microbubble's oscillation and deformation was also carried out, for an air bubble and for a shell-coated bubble in ultrasound field. As a result, it was confirmed that the CFD method developed in this study can be useful for analyzing an insonified microbubble showing nonspherical oscillation.