Abstract: Corresponding to thelower critical Mach number, Kuo and Tsien proposed in 1946 theconcept of upper critical Mach number. For two-dimensionalirrotational flow on a body, before the maximum of local Machnumber reaches a threshold, namely the upper critical Mach number,the irrotational supersonic flow still prevails, and only when thelocal Mach number exceeds the critical Mach number, theirrotational flow is eventually destroyed. Afterward, differentdesign techniques of supercritical airfoils were developed toaugment the drag-divergence Mach number, and the swept wings andarea rule were introduced to overcome `sonic barrier' and toreduce the peak drag near Mach 1. These achievements brought aboutthe tremendous development of aircraft industry in the lastcentury. As the advancement of computer technique andcomputational method, the solution algorithms for differentsimplified governing equations of fluiddynamics were constructed.At present, computational fluid dynamics based the Reynoldsaveraged Navier-Stokes equation have been widely applied to theevaluation of aerodynamic performances and the understanding ofcomplex flow mechanism. Aerodynamic optimization, fluid/structureinteraction and aeroacoustics et al have now become main researchdirections. To memorialize the 100 anniversary of Professor GuoYung-Huai, recent studies on computational aeroelasticity by ourresearch group were reviewed in the present paper.