Energetic charged-particle beams produced from ultrashort ultra-intense laser plasma interactions play a vital role in charged-particle radiography. When such an energetic beam penetrates through a foil target, its energy loss is negligible, and the main physics process is small-angle scattering. Owing to this scattering effect, charged-particle radiography of a target with a transversely distributed steep density gradient region will produce a modulation structure in the fluence distribution on the detection plane, which could be used to diagnose the steep density gradient region. In the past, the theoretical work on the scattering effect and the resulting modulation structure was done with Monte-Carlo simulations, which cost a lot of computing time and the studied parameter range was limited. In the present work, an analytical model is developed to deal with the scattering effect inside the target and the modulation structure on the detection plane in radiography, which can quickly present the results that coincide with Monte-Carlo simulations very well. By using this analytical model, the characteristics of modulation structures are analyzed. A dimensionless characteristic parameter related to radiography conditions is put forward, and its range determines different modulation structures and also the probability of diagnosing a steep density gradient region with a width $\lesssim $ 2 μm.