Very efficient generation of a high-charge electron beam by a laser pulse propagating in a self-trapping mode in near-critical density plasma makes it possible to produce a high yield of gamma rays for radiography of samples located deep in a dense medium. The three-dimensional particle-in-cell and Monte Carlo simulations performed with end-to-end modeling from laser–plasma interaction to the final gamma-imaging of deeply shielded objects located at distances up to several meters clearly demonstrate the promise of laser pulses of several hundred TW for single-shot radiography by using a high-performance scheme of electron acceleration in the laser pulse self-trapping regime. This is illustrated by two examples with the same laser–target design used for a bremsstrahlung gamma source and an all-optical nonlinear inverse Compton source.