A dynamical system is said to have the shadowing property provided that approximate orbits are well-approximated by true orbits. It has previously been established that for a continuum belonging to certain classes of continua, shadowing is a common, i.e. generic, property in its space of continuous self-maps. In particular, this is known for manifolds and for locally connected one-dimensional continua. We demonstrate that shadowing is a generic property in the space of continuous self-maps for any continuum which admits retractions onto graphs.