Shallow spherical shells are widely used in large structures, such as launch vehicles, nuclear containments, and gasholders. Studying scaled models of geometric and material distortion in the free vibration of large, thin-walled clamped shallow spherical shells is essential. First, frequency equations and natural frequency solutions for clamped shallow spherical shells are utilized to apply similarity transformation, leading to the derivation of generalized similarity conditions and scaling laws for the free vibration of these shells. The numerical approach is then validated by comparing the theoretical natural frequencies of clamped shallow spherical shells. Finally, geometric and material distortion similarity predictions for the free vibration of clamped shallow spherical shells with different rise-to-thickness ratios are investigated by numerical simulations. Results indicate that scaled models for clamped shallow spherical shells with different rise-to-thickness ratios, designed according to similarity conditions and incorporating the corresponding generalized similarity condition of mode shape and the natural frequency scaling relationship, can accurately predict the free vibration characteristics of the prototypes. For the free vibration of clamped shallow spherical shells with medium, small, and large rise-to-thickness ratios, in addition to meet the same mode shape, the distorted scaling laws also need to ensure that the scaling factors of rise-to-thickness ratio and Poisson's ratio equal 1, the scaling factor of Poisson's ratio is 1, and the rise-to-thickness ratios of scaled models and the prototype are no less than 25. The method and results of this study offer valuable insights for the design and experiments of scaled models for similar shells with thickness and material distortion.