Compressible aerodynamics is analyzed by the CIP/CCUP (constraint interpolation profile/CIP-combined unified procedure) method. The CIP method is feasible for an analysis of various phase change problems, those associated with compressible and incompressible flow areas. For aeroelastic problems based on CFD (computational fluid dynamics), the use of Lagrangian body-fitted grids is problematic because these grids increase the skewness of a mesh, or can be broken - even during structural motions. Therefore, a method embedding a physical boundary in a fixed Eulerian grid is appropriate compared to Lagrangian grids. In this paper, the CCUP method based on a pressure-based algorithm in which the pressure Poisson equation is modified to deal with compressible flows. A collocated grid system with the velocity components on the cell face obtained from the CIP interpolations is applied. Boundary condition for arbitrary surfaces are newly derived using a simple algebraic relationship based on the immersed boundary method. Far-field boundary condition is replaced with sponge layers. Several numerical benchmarking problems, in this case a wedge or a bump under transonic and supersonic flows, are tested to verify the code. Unsteady motions are directly applied to embedded solid areas. Finally, the steady and unsteady aerodynamics of airfoil sections are calculated and compared to reference data to validate the proposed method. (C) 2011 Elsevier Ltd. All rights reserved.