Shell structures are widely used in engineering, especially in aerospace and civil engineering. As a result, the study on dynamic behaviors of shell structures is crucial for engineering applications. Over the years, shell theory has undergone continuous improvement and development, leading to analytical solutions for specific shell structures. However, solving analytical solutions for complex shell structures with intricate shapes becomes highly challenging and even unattainable. Therefore, numerical methods like the finite element method (FEM) and the meshless method are employed for further solutions. The meshless method is a powerful complement to FEM, relying solely on nodal information for the formation of shape functions and enabling easy construction of higher-order smooth approximations. Consequently, it naturally holds an advantage in the numerical analysis of plate shell structures. Based on the 3D continuous shell theory and the moving least-squares (MLS) approximation, a meshless model for arbitrary shells is established in this paper. The MLS approximation is used not only for geometric surface interpolation, but also for displacement field approximation. The meshless equation governing the forced vibration of arbitrary shells is derived under Hamilton's principle and solved using the time-domain implicit Newmark method. The full transformation method is used to impose the essential boundary conditions. The code for the proposed method is developed in the MATLAB platform and used to compute several representative shell examples, obtaining the first ten natural frequencies of each shell type and the time history deflection at the center point under different pulse loads, considering both with and without damping. The calculated results are compared with ABAQUS solutions to verify the effectiveness and accuracy of the presented method. When using the meshless method to solve the forced vibration of arbitrary shell structures, it does not rely on grid partitioning. This enables effective analysis of various shell structures with different shapes, showcasing its strong adaptability and vast potential for applications.