The paper is concerned with the finite element analysis of hydroelastic stability of stationary or rotating elastic single and coaxial cylindrical shells subjected to compressible fluid flows having axial and tangential velocity components. The behavior of the flowing and rotating fluid is described in the framework of the potential theory. Consideration of elastic shells is based on the classical shell model. The results of the numerical analysis of shell stability for various boundary conditions, geometrical dimensions and different sizes of the annular gap between the outer and inner shells are discussed. It has been found that single and coaxial shells interacting with the combined fluid flows show qualitative differences in the dynamic behavior.