Abstract: Radiative fluid interfacial instability is a key scientific issue in fields such as inertial confinement fusion, aerospace, and national defense technology. The Richtmyer-Meshkov (RM) instability and turbulent mixing in converging geometries pose significant challenges to numerical simulation techniques. This paper focuses on the problem of a radiative shock wave interacting with a fluid interface in a converging cylindrical geometry. Unlike traditional hydrodynamic instabilities, the inclusion of radiative transfer fundamentally alters the energy distribution and wave dynamics, necessitating a more complex modeling approach. A corresponding mathematical and physical model is established, and numerical simulations are performed using the smoothed particle hydrodynamics method modified with a bilateral shock limiter, aiming to deepen the fundamental understanding of radiative effects in the interface mixing process. Through a dimensionless analysis of the one-dimensional radiative shock problem, key dimensionless parameters are identified, and the correctness of the mathematical model and numerical method is validated by simulating the Lowrie problem. On this basis, the evolution of the RM instability at a single-mode perturbed interface under a radiative shock in a converging cylindrical geometry is investigated, with a focus on the influence mechanisms of the flow-field material opacity and the radiative energy fraction. The results indicate that material opacity significantly alters the radiative diffusion effect of the radiative shock and thus plays an important role in the evolution of the RM instability. As opacity increases, the evolution of the RM instability gradually approaches the case without radiative effects. Although the radiative energy fraction exhibits a cubic amplification effect with the increase in the overall pressure field, its influence on the evolution of the RM instability is relatively minor, exerting a noticeable effect only when the opacity is low. In addition, this study confirms that the classical compressible theoretical model for RM instability remains applicable to problems involving radiative shocks.