This paper investigates the behavior of underwater shock wave around a cylindrical rigid body submerged in fluid. An analytical method is proposed for the investigation on propagation, reflection and diffraction of spherical and plane shock waves. The method is based on a linear theory utilizing modal superposition technique. Fluid-structure interaction for plane shock wave is also studied considering the frequency dependent radiation pressure induced by rigid body motion of the cylinder. Besides the analytical approaches, numerical analysis using explicit finite element method is performed and its results are compared with the analytical calculation results. Effects of element mesh size on the results are discussed. It has been found that the peak pressure on the front surface of the cylinder is as twice as that of the incident shock wave no matter whether the cylinder is fixed or free in fluid. The diffraction wave having considerable amplitude arrives at the opposite side of the cylinder and the magnitude depends on the decay period of the exponential incident shock wave.